diff --git a/python/plugins/processing/algs/qgis/StatisticsByCategories.py b/python/plugins/processing/algs/qgis/StatisticsByCategories.py
old mode 100644
new mode 100755
index dfe0097f06f..9e04aa20c9c
--- a/python/plugins/processing/algs/qgis/StatisticsByCategories.py
+++ b/python/plugins/processing/algs/qgis/StatisticsByCategories.py
@@ -28,6 +28,8 @@ __revision__ = '$Format:%H$'
 
 from qgis.core import (QgsProcessingParameterFeatureSource,
                        QgsStatisticalSummary,
+                       QgsDateTimeStatisticalSummary,
+                       QgsStringStatisticalSummary,
                        QgsFeatureRequest,
                        QgsProcessingParameterField,
                        QgsProcessingParameterFeatureSink,
@@ -36,13 +38,16 @@ from qgis.core import (QgsProcessingParameterFeatureSource,
                        QgsWkbTypes,
                        QgsCoordinateReferenceSystem,
                        QgsFeature,
-                       QgsFeatureSink)
+                       QgsFeatureSink,
+                       QgsProcessing,
+                       NULL)
 from qgis.PyQt.QtCore import QVariant
 from processing.algs.qgis.QgisAlgorithm import QgisAlgorithm
 
+from collections import defaultdict
+
 
 class StatisticsByCategories(QgisAlgorithm):
-
     INPUT = 'INPUT'
     VALUES_FIELD_NAME = 'VALUES_FIELD_NAME'
     CATEGORIES_FIELD_NAME = 'CATEGORIES_FIELD_NAME'
@@ -56,13 +61,16 @@ class StatisticsByCategories(QgisAlgorithm):
 
     def initAlgorithm(self, config=None):
         self.addParameter(QgsProcessingParameterFeatureSource(self.INPUT,
-                                                              self.tr('Input vector layer')))
+                                                              self.tr('Input vector layer'),
+                                                              types=[QgsProcessing.TypeVector]))
         self.addParameter(QgsProcessingParameterField(self.VALUES_FIELD_NAME,
-                                                      self.tr('Field to calculate statistics on'),
-                                                      parentLayerParameterName=self.INPUT, type=QgsProcessingParameterField.Numeric))
+                                                      self.tr(
+                                                          'Field to calculate statistics on (if empty, only count is calculated)'),
+                                                      parentLayerParameterName=self.INPUT, optional=True))
         self.addParameter(QgsProcessingParameterField(self.CATEGORIES_FIELD_NAME,
-                                                      self.tr('Field with categories'),
-                                                      parentLayerParameterName=self.INPUT, type=QgsProcessingParameterField.Any))
+                                                      self.tr('Field(s) with categories'),
+                                                      parentLayerParameterName=self.INPUT,
+                                                      type=QgsProcessingParameterField.Any, allowMultiple=True))
 
         self.addParameter(QgsProcessingParameterFeatureSink(self.OUTPUT, self.tr('Statistics by category')))
 
@@ -75,49 +83,213 @@ class StatisticsByCategories(QgisAlgorithm):
     def processAlgorithm(self, parameters, context, feedback):
         source = self.parameterAsSource(parameters, self.INPUT, context)
         value_field_name = self.parameterAsString(parameters, self.VALUES_FIELD_NAME, context)
-        category_field_name = self.parameterAsString(parameters, self.CATEGORIES_FIELD_NAME, context)
+        category_field_names = self.parameterAsFields(parameters, self.CATEGORIES_FIELD_NAME, context)
 
         value_field_index = source.fields().lookupField(value_field_name)
-        category_field_index = source.fields().lookupField(category_field_name)
+        if value_field_index >= 0:
+            value_field = source.fields().at(value_field_index)
+        else:
+            value_field = None
+        category_field_indexes = [source.fields().lookupField(n) for n in category_field_names]
 
-        features = source.getFeatures(QgsFeatureRequest().setFlags(QgsFeatureRequest.NoGeometry))
-        total = 100.0 / source.featureCount() if source.featureCount() else 0
-        values = {}
+        # generate output fields
+        fields = QgsFields()
+        for c in category_field_indexes:
+            fields.append(source.fields().at(c))
+
+        def addField(name):
+            """
+            Adds a field to the output, keeping the same data type as the value_field
+            """
+            field = value_field
+            field.setName(name)
+            fields.append(field)
+
+        if value_field is None:
+            field_type = 'none'
+            fields.append(QgsField('count', QVariant.Int))
+        elif value_field.isNumeric():
+            field_type = 'numeric'
+            fields.append(QgsField('count', QVariant.Int))
+            fields.append(QgsField('unique', QVariant.Int))
+            fields.append(QgsField('min', QVariant.Double))
+            fields.append(QgsField('max', QVariant.Double))
+            fields.append(QgsField('range', QVariant.Double))
+            fields.append(QgsField('sum', QVariant.Double))
+            fields.append(QgsField('mean', QVariant.Double))
+            fields.append(QgsField('median', QVariant.Double))
+            fields.append(QgsField('stddev', QVariant.Double))
+            fields.append(QgsField('minority', QVariant.Double))
+            fields.append(QgsField('majority', QVariant.Double))
+            fields.append(QgsField('q1', QVariant.Double))
+            fields.append(QgsField('q3', QVariant.Double))
+            fields.append(QgsField('iqr', QVariant.Double))
+        elif value_field.type() in (QVariant.Date, QVariant.Time, QVariant.DateTime):
+            field_type = 'datetime'
+            fields.append(QgsField('count', QVariant.Int))
+            fields.append(QgsField('unique', QVariant.Int))
+            fields.append(QgsField('empty', QVariant.Int))
+            fields.append(QgsField('filled', QVariant.Int))
+            # keep same data type for these fields
+            addField('min')
+            addField('max')
+        else:
+            field_type = 'string'
+            fields.append(QgsField('count', QVariant.Int))
+            fields.append(QgsField('unique', QVariant.Int))
+            fields.append(QgsField('empty', QVariant.Int))
+            fields.append(QgsField('filled', QVariant.Int))
+            # keep same data type for these fields
+            addField('min')
+            addField('max')
+            fields.append(QgsField('min_length', QVariant.Int))
+            fields.append(QgsField('max_length', QVariant.Int))
+            fields.append(QgsField('mean_length', QVariant.Double))
+
+        request = QgsFeatureRequest().setFlags(QgsFeatureRequest.NoGeometry)
+        if value_field is not None:
+            attrs = [value_field_index]
+        else:
+            attrs = []
+        attrs.extend(category_field_indexes)
+        request.setSubsetOfAttributes(attrs)
+        features = source.getFeatures(request)
+        total = 50.0 / source.featureCount() if source.featureCount() else 0
+        if field_type == 'none':
+            values = defaultdict(lambda: 0)
+        else:
+            values = defaultdict(list)
         for current, feat in enumerate(features):
             if feedback.isCanceled():
                 break
 
             feedback.setProgress(int(current * total))
             attrs = feat.attributes()
-            try:
-                value = float(attrs[value_field_index])
-                cat = attrs[category_field_index]
-                if cat not in values:
-                    values[cat] = []
-                values[cat].append(value)
-            except:
-                pass
-
-        fields = QgsFields()
-        fields.append(source.fields().at(category_field_index))
-        fields.append(QgsField('min', QVariant.Double))
-        fields.append(QgsField('max', QVariant.Double))
-        fields.append(QgsField('mean', QVariant.Double))
-        fields.append(QgsField('stddev', QVariant.Double))
-        fields.append(QgsField('sum', QVariant.Double))
-        fields.append(QgsField('count', QVariant.Int))
+            cat = tuple([attrs[c] for c in category_field_indexes])
+            if field_type == 'none':
+                values[cat] += 1
+                continue
+            if field_type == 'numeric':
+                if attrs[value_field_index] == NULL:
+                    continue
+                else:
+                    value = float(attrs[value_field_index])
+            elif field_type == 'string':
+                if attrs[value_field_index] == NULL:
+                    value = ''
+                else:
+                    value = str(attrs[value_field_index])
+            elif attrs[value_field_index] == NULL:
+                value = NULL
+            else:
+                value = attrs[value_field_index]
+            values[cat].append(value)
 
         (sink, dest_id) = self.parameterAsSink(parameters, self.OUTPUT, context,
                                                fields, QgsWkbTypes.NoGeometry, QgsCoordinateReferenceSystem())
 
-        stat = QgsStatisticalSummary(QgsStatisticalSummary.Min | QgsStatisticalSummary.Max |
-                                     QgsStatisticalSummary.Mean | QgsStatisticalSummary.StDevSample |
-                                     QgsStatisticalSummary.Sum | QgsStatisticalSummary.Count)
-
-        for (cat, v) in list(values.items()):
-            stat.calculate(v)
-            f = QgsFeature()
-            f.setAttributes([cat, stat.min(), stat.max(), stat.mean(), stat.sampleStDev(), stat.sum(), stat.count()])
-            sink.addFeature(f, QgsFeatureSink.FastInsert)
+        if field_type == 'none':
+            self.saveCounts(values, sink, feedback)
+        elif field_type == 'numeric':
+            self.calcNumericStats(values, sink, feedback)
+        elif field_type == 'datetime':
+            self.calcDateTimeStats(values, sink, feedback)
+        else:
+            self.calcStringStats(values, sink, feedback)
 
         return {self.OUTPUT: dest_id}
+
+    def saveCounts(self, values, sink, feedback):
+        total = 50.0 / len(values) if values else 0
+        current = 0
+        for cat, v in values.items():
+            if feedback.isCanceled():
+                break
+
+            feedback.setProgress(int(current * total) + 50)
+            f = QgsFeature()
+            f.setAttributes(list(cat) + [v])
+            sink.addFeature(f, QgsFeatureSink.FastInsert)
+            current += 1
+
+    def calcNumericStats(self, values, sink, feedback):
+        stat = QgsStatisticalSummary()
+
+        total = 50.0 / len(values) if values else 0
+        current = 0
+        for cat, v in values.items():
+            if feedback.isCanceled():
+                break
+
+            feedback.setProgress(int(current * total) + 50)
+
+            stat.calculate(v)
+            f = QgsFeature()
+            f.setAttributes(list(cat) + [stat.count(),
+                                         stat.variety(),
+                                         stat.min(),
+                                         stat.max(),
+                                         stat.range(),
+                                         stat.sum(),
+                                         stat.mean(),
+                                         stat.median(),
+                                         stat.stDev(),
+                                         stat.minority(),
+                                         stat.majority(),
+                                         stat.firstQuartile(),
+                                         stat.thirdQuartile(),
+                                         stat.interQuartileRange()])
+
+            sink.addFeature(f, QgsFeatureSink.FastInsert)
+            current += 1
+
+    def calcDateTimeStats(self, values, sink, feedback):
+        stat = QgsDateTimeStatisticalSummary()
+
+        total = 50.0 / len(values) if values else 0
+        current = 0
+        for cat, v in values.items():
+            if feedback.isCanceled():
+                break
+
+            feedback.setProgress(int(current * total) + 50)
+
+            stat.calculate(v)
+            f = QgsFeature()
+            f.setAttributes(list(cat) + [stat.count(),
+                                         stat.countDistinct(),
+                                         stat.countMissing(),
+                                         stat.count() - stat.countMissing(),
+                                         stat.statistic(QgsDateTimeStatisticalSummary.Min),
+                                         stat.statistic(QgsDateTimeStatisticalSummary.Max)
+                                         ])
+
+            sink.addFeature(f, QgsFeatureSink.FastInsert)
+            current += 1
+
+    def calcStringStats(self, values, sink, feedback):
+        stat = QgsStringStatisticalSummary()
+
+        total = 50.0 / len(values) if values else 0
+        current = 0
+        for cat, v in values.items():
+            if feedback.isCanceled():
+                break
+
+            feedback.setProgress(int(current * total) + 50)
+
+            stat.calculate(v)
+            f = QgsFeature()
+            f.setAttributes(list(cat) + [stat.count(),
+                                         stat.countDistinct(),
+                                         stat.countMissing(),
+                                         stat.count() - stat.countMissing(),
+                                         stat.min(),
+                                         stat.max(),
+                                         stat.minLength(),
+                                         stat.maxLength(),
+                                         stat.meanLength()
+                                         ])
+
+            sink.addFeature(f, QgsFeatureSink.FastInsert)
+            current += 1
diff --git a/python/plugins/processing/algs/qgis/scripts/Frequency_analysis.py b/python/plugins/processing/algs/qgis/scripts/Frequency_analysis.py
deleted file mode 100644
index e6c1885ee33..00000000000
--- a/python/plugins/processing/algs/qgis/scripts/Frequency_analysis.py
+++ /dev/null
@@ -1,47 +0,0 @@
-##Vector analysis=group
-
-#inputs
-
-##Input=source
-##Fields=field multiple Input
-##Frequency=sink table
-
-
-from processing.tools.vector import TableWriter
-from collections import defaultdict
-from qgis.core import QgsProcessingUtils, QgsFields, QgsField, QgsWkbTypes, QgsFeature
-from qgis.PyQt.QtCore import QVariant
-from processing.core.GeoAlgorithmExecutionException import GeoAlgorithmExecutionException
-
-inputFields = Input.fields()
-fieldIdxs = []
-out_fields = QgsFields()
-for f in Fields:
-    idx = inputFields.indexFromName(f)
-    if idx == -1:
-        raise GeoAlgorithmExecutionException('Field not found:' + f)
-    fieldIdxs.append(idx)
-    out_fields.append(inputFields.at(idx))
-
-out_fields.append(QgsField('FREQ', QVariant.Int))
-
-(sink, Frequency) = self.parameterAsSink(parameters, 'Frequency', context,
-                                         out_fields)
-
-counts = {}
-feats = Input.getFeatures()
-nFeats = Input.featureCount()
-counts = defaultdict(int)
-for i, feat in enumerate(feats):
-    feedback.setProgress(int(100 * i / nFeats))
-    if feedback.isCanceled():
-        break
-
-    attrs = feat.attributes()
-    clazz = tuple([attrs[i] for i in fieldIdxs])
-    counts[clazz] += 1
-
-for c in counts:
-    f = QgsFeature()
-    f.setAttributes(list(c) + [counts[c]])
-    sink.addFeature(f)
diff --git a/python/plugins/processing/algs/qgis/scripts/Number_of_unique_values_in_classes.py b/python/plugins/processing/algs/qgis/scripts/Number_of_unique_values_in_classes.py
deleted file mode 100644
index 5335c66e3f9..00000000000
--- a/python/plugins/processing/algs/qgis/scripts/Number_of_unique_values_in_classes.py
+++ /dev/null
@@ -1,52 +0,0 @@
-##Vector analysis=group
-
-# inputs
-
-
-##input=source
-##class_field=field input
-##value_field=field input
-##N_unique_values=sink
-
-
-from qgis.PyQt.QtCore import QVariant
-from qgis.core import QgsFeature, QgsField, QgsProcessingUtils
-
-fields = input.fields()
-fields.append(QgsField('UNIQ_COUNT', QVariant.Int))
-
-(sink, N_unique_values) = self.parameterAsSink(parameters, 'N_unique_values', context,
-                                               fields, input.wkbType(), input.sourceCrs())
-
-
-class_field_index = input.fields().lookupField(class_field)
-value_field_index = input.fields().lookupField(value_field)
-
-outFeat = QgsFeature()
-classes = {}
-feats = input.getFeatures()
-nFeat = input.featureCount()
-for n, inFeat in enumerate(feats):
-    if feedback.isCanceled():
-        break
-    feedback.setProgress(int(100 * n / nFeat))
-    attrs = inFeat.attributes()
-    clazz = attrs[class_field_index]
-    value = attrs[value_field_index]
-    if clazz not in classes:
-        classes[clazz] = []
-    if value not in classes[clazz]:
-        classes[clazz].append(value)
-
-feats = input.getFeatures()
-for n, inFeat in enumerate(feats):
-    if feedback.isCanceled():
-        break
-    feedback.setProgress(int(100 * n / nFeat))
-    inGeom = inFeat.geometry()
-    outFeat.setGeometry(inGeom)
-    attrs = inFeat.attributes()
-    clazz = attrs[class_field_index]
-    attrs.append(len(classes[clazz]))
-    outFeat.setAttributes(attrs)
-    sink.addFeature(outFeat)
diff --git a/python/plugins/processing/tests/testdata/expected/stats_by_cat_date.gfs b/python/plugins/processing/tests/testdata/expected/stats_by_cat_date.gfs
new file mode 100644
index 00000000000..1e740b97e92
--- /dev/null
+++ b/python/plugins/processing/tests/testdata/expected/stats_by_cat_date.gfs
@@ -0,0 +1,48 @@
+<GMLFeatureClassList>
+  <GMLFeatureClass>
+    <Name>stats_by_cat_date</Name>
+    <ElementPath>stats_by_cat_date</ElementPath>
+    <GeometryType>100</GeometryType>
+    <DatasetSpecificInfo>
+      <FeatureCount>4</FeatureCount>
+    </DatasetSpecificInfo>
+    <PropertyDefn>
+      <Name>date</Name>
+      <ElementPath>date</ElementPath>
+      <Type>String</Type>
+      <Width>10</Width>
+    </PropertyDefn>
+    <PropertyDefn>
+      <Name>count</Name>
+      <ElementPath>count</ElementPath>
+      <Type>Integer</Type>
+    </PropertyDefn>
+    <PropertyDefn>
+      <Name>unique</Name>
+      <ElementPath>unique</ElementPath>
+      <Type>Integer</Type>
+    </PropertyDefn>
+    <PropertyDefn>
+      <Name>empty</Name>
+      <ElementPath>empty</ElementPath>
+      <Type>Integer</Type>
+    </PropertyDefn>
+    <PropertyDefn>
+      <Name>filled</Name>
+      <ElementPath>filled</ElementPath>
+      <Type>Integer</Type>
+    </PropertyDefn>
+    <PropertyDefn>
+      <Name>min</Name>
+      <ElementPath>min</ElementPath>
+      <Type>String</Type>
+      <Width>10</Width>
+    </PropertyDefn>
+    <PropertyDefn>
+      <Name>max</Name>
+      <ElementPath>max</ElementPath>
+      <Type>String</Type>
+      <Width>10</Width>
+    </PropertyDefn>
+  </GMLFeatureClass>
+</GMLFeatureClassList>
diff --git a/python/plugins/processing/tests/testdata/expected/stats_by_cat_date.gml b/python/plugins/processing/tests/testdata/expected/stats_by_cat_date.gml
new file mode 100644
index 00000000000..27c0f84cb3b
--- /dev/null
+++ b/python/plugins/processing/tests/testdata/expected/stats_by_cat_date.gml
@@ -0,0 +1,50 @@
+<?xml version="1.0" encoding="utf-8" ?>
+<ogr:FeatureCollection
+     xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance"
+     xsi:schemaLocation=""
+     xmlns:ogr="http://ogr.maptools.org/"
+     xmlns:gml="http://www.opengis.net/gml">
+  <gml:boundedBy><gml:null>missing</gml:null></gml:boundedBy>
+                                                                                                                                                                                                                                                                                                
+  <gml:featureMember>
+    <ogr:stats_by_cat_date fid="stats_by_cat_date.0">
+      <ogr:date>2016/11/30</ogr:date>
+      <ogr:count>1</ogr:count>
+      <ogr:unique>1</ogr:unique>
+      <ogr:empty>0</ogr:empty>
+      <ogr:filled>1</ogr:filled>
+      <ogr:min>2016/11/30</ogr:min>
+      <ogr:max>2016/11/30</ogr:max>
+    </ogr:stats_by_cat_date>
+  </gml:featureMember>
+  <gml:featureMember>
+    <ogr:stats_by_cat_date fid="stats_by_cat_date.1">
+      <ogr:date>2016/11/10</ogr:date>
+      <ogr:count>1</ogr:count>
+      <ogr:unique>1</ogr:unique>
+      <ogr:empty>0</ogr:empty>
+      <ogr:filled>1</ogr:filled>
+      <ogr:min>2016/11/10</ogr:min>
+      <ogr:max>2016/11/10</ogr:max>
+    </ogr:stats_by_cat_date>
+  </gml:featureMember>
+  <gml:featureMember>
+    <ogr:stats_by_cat_date fid="stats_by_cat_date.2">
+      <ogr:count>1</ogr:count>
+      <ogr:unique>0</ogr:unique>
+      <ogr:empty>1</ogr:empty>
+      <ogr:filled>0</ogr:filled>
+    </ogr:stats_by_cat_date>
+  </gml:featureMember>
+  <gml:featureMember>
+    <ogr:stats_by_cat_date fid="stats_by_cat_date.3">
+      <ogr:date>2014/11/30</ogr:date>
+      <ogr:count>1</ogr:count>
+      <ogr:unique>1</ogr:unique>
+      <ogr:empty>0</ogr:empty>
+      <ogr:filled>1</ogr:filled>
+      <ogr:min>2014/11/30</ogr:min>
+      <ogr:max>2014/11/30</ogr:max>
+    </ogr:stats_by_cat_date>
+  </gml:featureMember>
+</ogr:FeatureCollection>
diff --git a/python/plugins/processing/tests/testdata/expected/stats_by_cat_float.gfs b/python/plugins/processing/tests/testdata/expected/stats_by_cat_float.gfs
new file mode 100644
index 00000000000..1069d98aeb8
--- /dev/null
+++ b/python/plugins/processing/tests/testdata/expected/stats_by_cat_float.gfs
@@ -0,0 +1,86 @@
+<GMLFeatureClassList>
+  <GMLFeatureClass>
+    <Name>stats_by_cat_float</Name>
+    <ElementPath>stats_by_cat_float</ElementPath>
+    <GeometryType>100</GeometryType>
+    <DatasetSpecificInfo>
+      <FeatureCount>5</FeatureCount>
+    </DatasetSpecificInfo>
+    <PropertyDefn>
+      <Name>name</Name>
+      <ElementPath>name</ElementPath>
+      <Type>String</Type>
+      <Width>2</Width>
+    </PropertyDefn>
+    <PropertyDefn>
+      <Name>count</Name>
+      <ElementPath>count</ElementPath>
+      <Type>Integer</Type>
+    </PropertyDefn>
+    <PropertyDefn>
+      <Name>unique</Name>
+      <ElementPath>unique</ElementPath>
+      <Type>Integer</Type>
+    </PropertyDefn>
+    <PropertyDefn>
+      <Name>min</Name>
+      <ElementPath>min</ElementPath>
+      <Type>Real</Type>
+    </PropertyDefn>
+    <PropertyDefn>
+      <Name>max</Name>
+      <ElementPath>max</ElementPath>
+      <Type>Real</Type>
+    </PropertyDefn>
+    <PropertyDefn>
+      <Name>range</Name>
+      <ElementPath>range</ElementPath>
+      <Type>Real</Type>
+    </PropertyDefn>
+    <PropertyDefn>
+      <Name>sum</Name>
+      <ElementPath>sum</ElementPath>
+      <Type>Real</Type>
+    </PropertyDefn>
+    <PropertyDefn>
+      <Name>mean</Name>
+      <ElementPath>mean</ElementPath>
+      <Type>Real</Type>
+    </PropertyDefn>
+    <PropertyDefn>
+      <Name>median</Name>
+      <ElementPath>median</ElementPath>
+      <Type>Real</Type>
+    </PropertyDefn>
+    <PropertyDefn>
+      <Name>stddev</Name>
+      <ElementPath>stddev</ElementPath>
+      <Type>Real</Type>
+    </PropertyDefn>
+    <PropertyDefn>
+      <Name>minority</Name>
+      <ElementPath>minority</ElementPath>
+      <Type>Real</Type>
+    </PropertyDefn>
+    <PropertyDefn>
+      <Name>majority</Name>
+      <ElementPath>majority</ElementPath>
+      <Type>Real</Type>
+    </PropertyDefn>
+    <PropertyDefn>
+      <Name>q1</Name>
+      <ElementPath>q1</ElementPath>
+      <Type>Real</Type>
+    </PropertyDefn>
+    <PropertyDefn>
+      <Name>q3</Name>
+      <ElementPath>q3</ElementPath>
+      <Type>Real</Type>
+    </PropertyDefn>
+    <PropertyDefn>
+      <Name>iqr</Name>
+      <ElementPath>iqr</ElementPath>
+      <Type>Real</Type>
+    </PropertyDefn>
+  </GMLFeatureClass>
+</GMLFeatureClassList>
diff --git a/python/plugins/processing/tests/testdata/expected/stats_by_cat_float.gml b/python/plugins/processing/tests/testdata/expected/stats_by_cat_float.gml
new file mode 100644
index 00000000000..1fa21ebeadc
--- /dev/null
+++ b/python/plugins/processing/tests/testdata/expected/stats_by_cat_float.gml
@@ -0,0 +1,103 @@
+<?xml version="1.0" encoding="utf-8" ?>
+<ogr:FeatureCollection
+     xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance"
+     xsi:schemaLocation=""
+     xmlns:ogr="http://ogr.maptools.org/"
+     xmlns:gml="http://www.opengis.net/gml">
+  <gml:boundedBy><gml:null>missing</gml:null></gml:boundedBy>
+                                                                                                                                                                                                                                                                                                
+  <gml:featureMember>
+    <ogr:stats_by_cat_float fid="stats_by_cat_float.0">
+      <ogr:name>aa</ogr:name>
+      <ogr:count>2</ogr:count>
+      <ogr:unique>2</ogr:unique>
+      <ogr:min>3.33</ogr:min>
+      <ogr:max>44.123456</ogr:max>
+      <ogr:range>40.793456</ogr:range>
+      <ogr:sum>47.453456</ogr:sum>
+      <ogr:mean>23.726728</ogr:mean>
+      <ogr:median>23.726728</ogr:median>
+      <ogr:stddev>20.396728</ogr:stddev>
+      <ogr:minority>3.33</ogr:minority>
+      <ogr:majority>3.33</ogr:majority>
+      <ogr:q1>3.33</ogr:q1>
+      <ogr:q3>44.123456</ogr:q3>
+      <ogr:iqr>40.793456</ogr:iqr>
+    </ogr:stats_by_cat_float>
+  </gml:featureMember>
+  <gml:featureMember>
+    <ogr:stats_by_cat_float fid="stats_by_cat_float.1">
+      <ogr:name>dd</ogr:name>
+      <ogr:count>1</ogr:count>
+      <ogr:unique>1</ogr:unique>
+      <ogr:min>0</ogr:min>
+      <ogr:max>0</ogr:max>
+      <ogr:range>0</ogr:range>
+      <ogr:sum>0</ogr:sum>
+      <ogr:mean>0</ogr:mean>
+      <ogr:median>0</ogr:median>
+      <ogr:stddev>0</ogr:stddev>
+      <ogr:minority>0</ogr:minority>
+      <ogr:majority>0</ogr:majority>
+      <ogr:q1>0</ogr:q1>
+      <ogr:q3>0</ogr:q3>
+      <ogr:iqr>0</ogr:iqr>
+    </ogr:stats_by_cat_float>
+  </gml:featureMember>
+  <gml:featureMember>
+    <ogr:stats_by_cat_float fid="stats_by_cat_float.2">
+      <ogr:name>bb</ogr:name>
+      <ogr:count>4</ogr:count>
+      <ogr:unique>1</ogr:unique>
+      <ogr:min>0.123</ogr:min>
+      <ogr:max>0.123</ogr:max>
+      <ogr:range>0</ogr:range>
+      <ogr:sum>0.492</ogr:sum>
+      <ogr:mean>0.123</ogr:mean>
+      <ogr:median>0.123</ogr:median>
+      <ogr:stddev>0</ogr:stddev>
+      <ogr:minority>0.123</ogr:minority>
+      <ogr:majority>0.123</ogr:majority>
+      <ogr:q1>0.123</ogr:q1>
+      <ogr:q3>0.123</ogr:q3>
+      <ogr:iqr>0</ogr:iqr>
+    </ogr:stats_by_cat_float>
+  </gml:featureMember>
+  <gml:featureMember>
+    <ogr:stats_by_cat_float fid="stats_by_cat_float.3">
+      <ogr:count>1</ogr:count>
+      <ogr:unique>1</ogr:unique>
+      <ogr:min>-100291.43213</ogr:min>
+      <ogr:max>-100291.43213</ogr:max>
+      <ogr:range>0</ogr:range>
+      <ogr:sum>-100291.43213</ogr:sum>
+      <ogr:mean>-100291.43213</ogr:mean>
+      <ogr:median>-100291.43213</ogr:median>
+      <ogr:stddev>0</ogr:stddev>
+      <ogr:minority>-100291.43213</ogr:minority>
+      <ogr:majority>-100291.43213</ogr:majority>
+      <ogr:q1>-100291.43213</ogr:q1>
+      <ogr:q3>-100291.43213</ogr:q3>
+      <ogr:iqr>0</ogr:iqr>
+    </ogr:stats_by_cat_float>
+  </gml:featureMember>
+  <gml:featureMember>
+    <ogr:stats_by_cat_float fid="stats_by_cat_float.4">
+      <ogr:name>cc</ogr:name>
+      <ogr:count>1</ogr:count>
+      <ogr:unique>1</ogr:unique>
+      <ogr:min>0.123</ogr:min>
+      <ogr:max>0.123</ogr:max>
+      <ogr:range>0</ogr:range>
+      <ogr:sum>0.123</ogr:sum>
+      <ogr:mean>0.123</ogr:mean>
+      <ogr:median>0.123</ogr:median>
+      <ogr:stddev>0</ogr:stddev>
+      <ogr:minority>0.123</ogr:minority>
+      <ogr:majority>0.123</ogr:majority>
+      <ogr:q1>0.123</ogr:q1>
+      <ogr:q3>0.123</ogr:q3>
+      <ogr:iqr>0</ogr:iqr>
+    </ogr:stats_by_cat_float>
+  </gml:featureMember>
+</ogr:FeatureCollection>
diff --git a/python/plugins/processing/tests/testdata/expected/stats_by_cat_no_value.gfs b/python/plugins/processing/tests/testdata/expected/stats_by_cat_no_value.gfs
new file mode 100644
index 00000000000..b8719d76b93
--- /dev/null
+++ b/python/plugins/processing/tests/testdata/expected/stats_by_cat_no_value.gfs
@@ -0,0 +1,26 @@
+<GMLFeatureClassList>
+  <GMLFeatureClass>
+    <Name>stats_by_cat_no_value</Name>
+    <ElementPath>stats_by_cat_no_value</ElementPath>
+    <GeometryType>100</GeometryType>
+    <DatasetSpecificInfo>
+      <FeatureCount>6</FeatureCount>
+    </DatasetSpecificInfo>
+    <PropertyDefn>
+      <Name>intval</Name>
+      <ElementPath>intval</ElementPath>
+      <Type>Integer</Type>
+    </PropertyDefn>
+    <PropertyDefn>
+      <Name>name</Name>
+      <ElementPath>name</ElementPath>
+      <Type>String</Type>
+      <Width>2</Width>
+    </PropertyDefn>
+    <PropertyDefn>
+      <Name>count</Name>
+      <ElementPath>count</ElementPath>
+      <Type>Integer</Type>
+    </PropertyDefn>
+  </GMLFeatureClass>
+</GMLFeatureClassList>
diff --git a/python/plugins/processing/tests/testdata/expected/stats_by_cat_no_value.gml b/python/plugins/processing/tests/testdata/expected/stats_by_cat_no_value.gml
new file mode 100644
index 00000000000..5590c2625a4
--- /dev/null
+++ b/python/plugins/processing/tests/testdata/expected/stats_by_cat_no_value.gml
@@ -0,0 +1,48 @@
+<?xml version="1.0" encoding="utf-8" ?>
+<ogr:FeatureCollection
+     xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance"
+     xsi:schemaLocation=""
+     xmlns:ogr="http://ogr.maptools.org/"
+     xmlns:gml="http://www.opengis.net/gml">
+  <gml:boundedBy><gml:null>missing</gml:null></gml:boundedBy>
+                                                                                                                                                                                                                                                                                                
+  <gml:featureMember>
+    <ogr:stats_by_cat_no_value fid="stats_by_cat_no_value.0">
+      <ogr:intval>1</ogr:intval>
+      <ogr:name>aa</ogr:name>
+      <ogr:count>2</ogr:count>
+    </ogr:stats_by_cat_no_value>
+  </gml:featureMember>
+  <gml:featureMember>
+    <ogr:stats_by_cat_no_value fid="stats_by_cat_no_value.1">
+      <ogr:name>dd</ogr:name>
+      <ogr:count>2</ogr:count>
+    </ogr:stats_by_cat_no_value>
+  </gml:featureMember>
+  <gml:featureMember>
+    <ogr:stats_by_cat_no_value fid="stats_by_cat_no_value.2">
+      <ogr:intval>1</ogr:intval>
+      <ogr:name>bb</ogr:name>
+      <ogr:count>3</ogr:count>
+    </ogr:stats_by_cat_no_value>
+  </gml:featureMember>
+  <gml:featureMember>
+    <ogr:stats_by_cat_no_value fid="stats_by_cat_no_value.3">
+      <ogr:intval>120</ogr:intval>
+      <ogr:count>1</ogr:count>
+    </ogr:stats_by_cat_no_value>
+  </gml:featureMember>
+  <gml:featureMember>
+    <ogr:stats_by_cat_no_value fid="stats_by_cat_no_value.4">
+      <ogr:name>cc</ogr:name>
+      <ogr:count>1</ogr:count>
+    </ogr:stats_by_cat_no_value>
+  </gml:featureMember>
+  <gml:featureMember>
+    <ogr:stats_by_cat_no_value fid="stats_by_cat_no_value.5">
+      <ogr:intval>2</ogr:intval>
+      <ogr:name>bb</ogr:name>
+      <ogr:count>1</ogr:count>
+    </ogr:stats_by_cat_no_value>
+  </gml:featureMember>
+</ogr:FeatureCollection>
diff --git a/python/plugins/processing/tests/testdata/expected/stats_by_cat_string.gfs b/python/plugins/processing/tests/testdata/expected/stats_by_cat_string.gfs
new file mode 100644
index 00000000000..0fb2358c926
--- /dev/null
+++ b/python/plugins/processing/tests/testdata/expected/stats_by_cat_string.gfs
@@ -0,0 +1,62 @@
+<GMLFeatureClassList>
+  <GMLFeatureClass>
+    <Name>stats_by_cat_string</Name>
+    <ElementPath>stats_by_cat_string</ElementPath>
+    <GeometryType>100</GeometryType>
+    <DatasetSpecificInfo>
+      <FeatureCount>4</FeatureCount>
+    </DatasetSpecificInfo>
+    <PropertyDefn>
+      <Name>intval</Name>
+      <ElementPath>intval</ElementPath>
+      <Type>Integer</Type>
+    </PropertyDefn>
+    <PropertyDefn>
+      <Name>count</Name>
+      <ElementPath>count</ElementPath>
+      <Type>Integer</Type>
+    </PropertyDefn>
+    <PropertyDefn>
+      <Name>unique</Name>
+      <ElementPath>unique</ElementPath>
+      <Type>Integer</Type>
+    </PropertyDefn>
+    <PropertyDefn>
+      <Name>empty</Name>
+      <ElementPath>empty</ElementPath>
+      <Type>Integer</Type>
+    </PropertyDefn>
+    <PropertyDefn>
+      <Name>filled</Name>
+      <ElementPath>filled</ElementPath>
+      <Type>Integer</Type>
+    </PropertyDefn>
+    <PropertyDefn>
+      <Name>min</Name>
+      <ElementPath>min</ElementPath>
+      <Type>String</Type>
+      <Width>2</Width>
+    </PropertyDefn>
+    <PropertyDefn>
+      <Name>max</Name>
+      <ElementPath>max</ElementPath>
+      <Type>String</Type>
+      <Width>2</Width>
+    </PropertyDefn>
+    <PropertyDefn>
+      <Name>min_length</Name>
+      <ElementPath>min_length</ElementPath>
+      <Type>Integer</Type>
+    </PropertyDefn>
+    <PropertyDefn>
+      <Name>max_length</Name>
+      <ElementPath>max_length</ElementPath>
+      <Type>Integer</Type>
+    </PropertyDefn>
+    <PropertyDefn>
+      <Name>mean_length</Name>
+      <ElementPath>mean_length</ElementPath>
+      <Type>Integer</Type>
+    </PropertyDefn>
+  </GMLFeatureClass>
+</GMLFeatureClassList>
diff --git a/python/plugins/processing/tests/testdata/expected/stats_by_cat_string.gml b/python/plugins/processing/tests/testdata/expected/stats_by_cat_string.gml
new file mode 100644
index 00000000000..600e578de7d
--- /dev/null
+++ b/python/plugins/processing/tests/testdata/expected/stats_by_cat_string.gml
@@ -0,0 +1,64 @@
+<?xml version="1.0" encoding="utf-8" ?>
+<ogr:FeatureCollection
+     xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance"
+     xsi:schemaLocation=""
+     xmlns:ogr="http://ogr.maptools.org/"
+     xmlns:gml="http://www.opengis.net/gml">
+  <gml:boundedBy><gml:null>missing</gml:null></gml:boundedBy>
+                                                                                                                                                                                                                                                                                                
+  <gml:featureMember>
+    <ogr:stats_by_cat_string fid="stats_by_cat_string.0">
+      <ogr:intval>1</ogr:intval>
+      <ogr:count>5</ogr:count>
+      <ogr:unique>2</ogr:unique>
+      <ogr:empty>0</ogr:empty>
+      <ogr:filled>5</ogr:filled>
+      <ogr:min>aa</ogr:min>
+      <ogr:max>bb</ogr:max>
+      <ogr:min_length>2</ogr:min_length>
+      <ogr:max_length>2</ogr:max_length>
+      <ogr:mean_length>2</ogr:mean_length>
+    </ogr:stats_by_cat_string>
+  </gml:featureMember>
+  <gml:featureMember>
+    <ogr:stats_by_cat_string fid="stats_by_cat_string.1">
+      <ogr:count>3</ogr:count>
+      <ogr:unique>2</ogr:unique>
+      <ogr:empty>0</ogr:empty>
+      <ogr:filled>3</ogr:filled>
+      <ogr:min>cc</ogr:min>
+      <ogr:max>dd</ogr:max>
+      <ogr:min_length>2</ogr:min_length>
+      <ogr:max_length>2</ogr:max_length>
+      <ogr:mean_length>2</ogr:mean_length>
+    </ogr:stats_by_cat_string>
+  </gml:featureMember>
+  <gml:featureMember>
+    <ogr:stats_by_cat_string fid="stats_by_cat_string.2">
+      <ogr:intval>120</ogr:intval>
+      <ogr:count>1</ogr:count>
+      <ogr:unique>1</ogr:unique>
+      <ogr:empty>1</ogr:empty>
+      <ogr:filled>0</ogr:filled>
+      <ogr:min></ogr:min>
+      <ogr:max></ogr:max>
+      <ogr:min_length>0</ogr:min_length>
+      <ogr:max_length>0</ogr:max_length>
+      <ogr:mean_length>0</ogr:mean_length>
+    </ogr:stats_by_cat_string>
+  </gml:featureMember>
+  <gml:featureMember>
+    <ogr:stats_by_cat_string fid="stats_by_cat_string.3">
+      <ogr:intval>2</ogr:intval>
+      <ogr:count>1</ogr:count>
+      <ogr:unique>1</ogr:unique>
+      <ogr:empty>0</ogr:empty>
+      <ogr:filled>1</ogr:filled>
+      <ogr:min>bb</ogr:min>
+      <ogr:max>bb</ogr:max>
+      <ogr:min_length>2</ogr:min_length>
+      <ogr:max_length>2</ogr:max_length>
+      <ogr:mean_length>2</ogr:mean_length>
+    </ogr:stats_by_cat_string>
+  </gml:featureMember>
+</ogr:FeatureCollection>
diff --git a/python/plugins/processing/tests/testdata/expected/stats_by_cat_two_fields.gfs b/python/plugins/processing/tests/testdata/expected/stats_by_cat_two_fields.gfs
new file mode 100644
index 00000000000..348c809ee01
--- /dev/null
+++ b/python/plugins/processing/tests/testdata/expected/stats_by_cat_two_fields.gfs
@@ -0,0 +1,91 @@
+<GMLFeatureClassList>
+  <GMLFeatureClass>
+    <Name>stats_by_cat_two_fields</Name>
+    <ElementPath>stats_by_cat_two_fields</ElementPath>
+    <GeometryType>100</GeometryType>
+    <DatasetSpecificInfo>
+      <FeatureCount>6</FeatureCount>
+    </DatasetSpecificInfo>
+    <PropertyDefn>
+      <Name>intval</Name>
+      <ElementPath>intval</ElementPath>
+      <Type>Integer</Type>
+    </PropertyDefn>
+    <PropertyDefn>
+      <Name>name</Name>
+      <ElementPath>name</ElementPath>
+      <Type>String</Type>
+      <Width>2</Width>
+    </PropertyDefn>
+    <PropertyDefn>
+      <Name>count</Name>
+      <ElementPath>count</ElementPath>
+      <Type>Integer</Type>
+    </PropertyDefn>
+    <PropertyDefn>
+      <Name>unique</Name>
+      <ElementPath>unique</ElementPath>
+      <Type>Integer</Type>
+    </PropertyDefn>
+    <PropertyDefn>
+      <Name>min</Name>
+      <ElementPath>min</ElementPath>
+      <Type>Real</Type>
+    </PropertyDefn>
+    <PropertyDefn>
+      <Name>max</Name>
+      <ElementPath>max</ElementPath>
+      <Type>Real</Type>
+    </PropertyDefn>
+    <PropertyDefn>
+      <Name>range</Name>
+      <ElementPath>range</ElementPath>
+      <Type>Real</Type>
+    </PropertyDefn>
+    <PropertyDefn>
+      <Name>sum</Name>
+      <ElementPath>sum</ElementPath>
+      <Type>Real</Type>
+    </PropertyDefn>
+    <PropertyDefn>
+      <Name>mean</Name>
+      <ElementPath>mean</ElementPath>
+      <Type>Real</Type>
+    </PropertyDefn>
+    <PropertyDefn>
+      <Name>median</Name>
+      <ElementPath>median</ElementPath>
+      <Type>Real</Type>
+    </PropertyDefn>
+    <PropertyDefn>
+      <Name>stddev</Name>
+      <ElementPath>stddev</ElementPath>
+      <Type>Real</Type>
+    </PropertyDefn>
+    <PropertyDefn>
+      <Name>minority</Name>
+      <ElementPath>minority</ElementPath>
+      <Type>Real</Type>
+    </PropertyDefn>
+    <PropertyDefn>
+      <Name>majority</Name>
+      <ElementPath>majority</ElementPath>
+      <Type>Real</Type>
+    </PropertyDefn>
+    <PropertyDefn>
+      <Name>q1</Name>
+      <ElementPath>q1</ElementPath>
+      <Type>Real</Type>
+    </PropertyDefn>
+    <PropertyDefn>
+      <Name>q3</Name>
+      <ElementPath>q3</ElementPath>
+      <Type>Real</Type>
+    </PropertyDefn>
+    <PropertyDefn>
+      <Name>iqr</Name>
+      <ElementPath>iqr</ElementPath>
+      <Type>Real</Type>
+    </PropertyDefn>
+  </GMLFeatureClass>
+</GMLFeatureClassList>
diff --git a/python/plugins/processing/tests/testdata/expected/stats_by_cat_two_fields.gml b/python/plugins/processing/tests/testdata/expected/stats_by_cat_two_fields.gml
new file mode 100644
index 00000000000..e8668bfdc2b
--- /dev/null
+++ b/python/plugins/processing/tests/testdata/expected/stats_by_cat_two_fields.gml
@@ -0,0 +1,126 @@
+<?xml version="1.0" encoding="utf-8" ?>
+<ogr:FeatureCollection
+     xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance"
+     xsi:schemaLocation=""
+     xmlns:ogr="http://ogr.maptools.org/"
+     xmlns:gml="http://www.opengis.net/gml">
+  <gml:boundedBy><gml:null>missing</gml:null></gml:boundedBy>
+                                                                                                                                                                                                                                                                                                
+  <gml:featureMember>
+    <ogr:stats_by_cat_two_fields fid="stats_by_cat_two_fields.0">
+      <ogr:intval>1</ogr:intval>
+      <ogr:name>aa</ogr:name>
+      <ogr:count>2</ogr:count>
+      <ogr:unique>2</ogr:unique>
+      <ogr:min>3.33</ogr:min>
+      <ogr:max>44.123456</ogr:max>
+      <ogr:range>40.793456</ogr:range>
+      <ogr:sum>47.453456</ogr:sum>
+      <ogr:mean>23.726728</ogr:mean>
+      <ogr:median>23.726728</ogr:median>
+      <ogr:stddev>20.396728</ogr:stddev>
+      <ogr:minority>3.33</ogr:minority>
+      <ogr:majority>3.33</ogr:majority>
+      <ogr:q1>3.33</ogr:q1>
+      <ogr:q3>44.123456</ogr:q3>
+      <ogr:iqr>40.793456</ogr:iqr>
+    </ogr:stats_by_cat_two_fields>
+  </gml:featureMember>
+  <gml:featureMember>
+    <ogr:stats_by_cat_two_fields fid="stats_by_cat_two_fields.1">
+      <ogr:name>dd</ogr:name>
+      <ogr:count>1</ogr:count>
+      <ogr:unique>1</ogr:unique>
+      <ogr:min>0</ogr:min>
+      <ogr:max>0</ogr:max>
+      <ogr:range>0</ogr:range>
+      <ogr:sum>0</ogr:sum>
+      <ogr:mean>0</ogr:mean>
+      <ogr:median>0</ogr:median>
+      <ogr:stddev>0</ogr:stddev>
+      <ogr:minority>0</ogr:minority>
+      <ogr:majority>0</ogr:majority>
+      <ogr:q1>0</ogr:q1>
+      <ogr:q3>0</ogr:q3>
+      <ogr:iqr>0</ogr:iqr>
+    </ogr:stats_by_cat_two_fields>
+  </gml:featureMember>
+  <gml:featureMember>
+    <ogr:stats_by_cat_two_fields fid="stats_by_cat_two_fields.2">
+      <ogr:intval>1</ogr:intval>
+      <ogr:name>bb</ogr:name>
+      <ogr:count>3</ogr:count>
+      <ogr:unique>1</ogr:unique>
+      <ogr:min>0.123</ogr:min>
+      <ogr:max>0.123</ogr:max>
+      <ogr:range>0</ogr:range>
+      <ogr:sum>0.369</ogr:sum>
+      <ogr:mean>0.123</ogr:mean>
+      <ogr:median>0.123</ogr:median>
+      <ogr:stddev>0</ogr:stddev>
+      <ogr:minority>0.123</ogr:minority>
+      <ogr:majority>0.123</ogr:majority>
+      <ogr:q1>0.123</ogr:q1>
+      <ogr:q3>0.123</ogr:q3>
+      <ogr:iqr>0</ogr:iqr>
+    </ogr:stats_by_cat_two_fields>
+  </gml:featureMember>
+  <gml:featureMember>
+    <ogr:stats_by_cat_two_fields fid="stats_by_cat_two_fields.3">
+      <ogr:intval>120</ogr:intval>
+      <ogr:count>1</ogr:count>
+      <ogr:unique>1</ogr:unique>
+      <ogr:min>-100291.43213</ogr:min>
+      <ogr:max>-100291.43213</ogr:max>
+      <ogr:range>0</ogr:range>
+      <ogr:sum>-100291.43213</ogr:sum>
+      <ogr:mean>-100291.43213</ogr:mean>
+      <ogr:median>-100291.43213</ogr:median>
+      <ogr:stddev>0</ogr:stddev>
+      <ogr:minority>-100291.43213</ogr:minority>
+      <ogr:majority>-100291.43213</ogr:majority>
+      <ogr:q1>-100291.43213</ogr:q1>
+      <ogr:q3>-100291.43213</ogr:q3>
+      <ogr:iqr>0</ogr:iqr>
+    </ogr:stats_by_cat_two_fields>
+  </gml:featureMember>
+  <gml:featureMember>
+    <ogr:stats_by_cat_two_fields fid="stats_by_cat_two_fields.4">
+      <ogr:name>cc</ogr:name>
+      <ogr:count>1</ogr:count>
+      <ogr:unique>1</ogr:unique>
+      <ogr:min>0.123</ogr:min>
+      <ogr:max>0.123</ogr:max>
+      <ogr:range>0</ogr:range>
+      <ogr:sum>0.123</ogr:sum>
+      <ogr:mean>0.123</ogr:mean>
+      <ogr:median>0.123</ogr:median>
+      <ogr:stddev>0</ogr:stddev>
+      <ogr:minority>0.123</ogr:minority>
+      <ogr:majority>0.123</ogr:majority>
+      <ogr:q1>0.123</ogr:q1>
+      <ogr:q3>0.123</ogr:q3>
+      <ogr:iqr>0</ogr:iqr>
+    </ogr:stats_by_cat_two_fields>
+  </gml:featureMember>
+  <gml:featureMember>
+    <ogr:stats_by_cat_two_fields fid="stats_by_cat_two_fields.5">
+      <ogr:intval>2</ogr:intval>
+      <ogr:name>bb</ogr:name>
+      <ogr:count>1</ogr:count>
+      <ogr:unique>1</ogr:unique>
+      <ogr:min>0.123</ogr:min>
+      <ogr:max>0.123</ogr:max>
+      <ogr:range>0</ogr:range>
+      <ogr:sum>0.123</ogr:sum>
+      <ogr:mean>0.123</ogr:mean>
+      <ogr:median>0.123</ogr:median>
+      <ogr:stddev>0</ogr:stddev>
+      <ogr:minority>0.123</ogr:minority>
+      <ogr:majority>0.123</ogr:majority>
+      <ogr:q1>0.123</ogr:q1>
+      <ogr:q3>0.123</ogr:q3>
+      <ogr:iqr>0</ogr:iqr>
+    </ogr:stats_by_cat_two_fields>
+  </gml:featureMember>
+</ogr:FeatureCollection>
diff --git a/python/plugins/processing/tests/testdata/expected/stats_by_category.gfs b/python/plugins/processing/tests/testdata/expected/stats_by_category.gfs
index ba663caa0c0..99c98501a5b 100644
--- a/python/plugins/processing/tests/testdata/expected/stats_by_category.gfs
+++ b/python/plugins/processing/tests/testdata/expected/stats_by_category.gfs
@@ -11,6 +11,16 @@
       <ElementPath>id2</ElementPath>
       <Type>Integer</Type>
     </PropertyDefn>
+    <PropertyDefn>
+      <Name>count</Name>
+      <ElementPath>count</ElementPath>
+      <Type>Integer</Type>
+    </PropertyDefn>
+    <PropertyDefn>
+      <Name>unique</Name>
+      <ElementPath>unique</ElementPath>
+      <Type>Integer</Type>
+    </PropertyDefn>
     <PropertyDefn>
       <Name>min</Name>
       <ElementPath>min</ElementPath>
@@ -21,24 +31,54 @@
       <ElementPath>max</ElementPath>
       <Type>Integer</Type>
     </PropertyDefn>
+    <PropertyDefn>
+      <Name>range</Name>
+      <ElementPath>range</ElementPath>
+      <Type>Integer</Type>
+    </PropertyDefn>
+    <PropertyDefn>
+      <Name>sum</Name>
+      <ElementPath>sum</ElementPath>
+      <Type>Integer</Type>
+    </PropertyDefn>
     <PropertyDefn>
       <Name>mean</Name>
       <ElementPath>mean</ElementPath>
       <Type>Real</Type>
     </PropertyDefn>
+    <PropertyDefn>
+      <Name>median</Name>
+      <ElementPath>median</ElementPath>
+      <Type>Real</Type>
+    </PropertyDefn>
     <PropertyDefn>
       <Name>stddev</Name>
       <ElementPath>stddev</ElementPath>
       <Type>Real</Type>
     </PropertyDefn>
     <PropertyDefn>
-      <Name>sum</Name>
-      <ElementPath>sum</ElementPath>
+      <Name>minority</Name>
+      <ElementPath>minority</ElementPath>
       <Type>Integer</Type>
     </PropertyDefn>
     <PropertyDefn>
-      <Name>count</Name>
-      <ElementPath>count</ElementPath>
+      <Name>majority</Name>
+      <ElementPath>majority</ElementPath>
+      <Type>Integer</Type>
+    </PropertyDefn>
+    <PropertyDefn>
+      <Name>q1</Name>
+      <ElementPath>q1</ElementPath>
+      <Type>Integer</Type>
+    </PropertyDefn>
+    <PropertyDefn>
+      <Name>q3</Name>
+      <ElementPath>q3</ElementPath>
+      <Type>Integer</Type>
+    </PropertyDefn>
+    <PropertyDefn>
+      <Name>iqr</Name>
+      <ElementPath>iqr</ElementPath>
       <Type>Integer</Type>
     </PropertyDefn>
   </GMLFeatureClass>
diff --git a/python/plugins/processing/tests/testdata/expected/stats_by_category.gml b/python/plugins/processing/tests/testdata/expected/stats_by_category.gml
index 4647a986f75..7fcd964d673 100644
--- a/python/plugins/processing/tests/testdata/expected/stats_by_category.gml
+++ b/python/plugins/processing/tests/testdata/expected/stats_by_category.gml
@@ -9,34 +9,58 @@
   <gml:featureMember>
     <ogr:stats_by_category fid="stats_by_category.0">
       <ogr:id2>2</ogr:id2>
+      <ogr:count>2</ogr:count>
+      <ogr:unique>2</ogr:unique>
       <ogr:min>1</ogr:min>
       <ogr:max>4</ogr:max>
-      <ogr:mean>2.5</ogr:mean>
-      <ogr:stddev>2.12132034355964</ogr:stddev>
+      <ogr:range>3</ogr:range>
       <ogr:sum>5</ogr:sum>
-      <ogr:count>2</ogr:count>
+      <ogr:mean>2.5</ogr:mean>
+      <ogr:median>2.5</ogr:median>
+      <ogr:stddev>1.5</ogr:stddev>
+      <ogr:minority>1</ogr:minority>
+      <ogr:majority>1</ogr:majority>
+      <ogr:q1>1</ogr:q1>
+      <ogr:q3>4</ogr:q3>
+      <ogr:iqr>3</ogr:iqr>
     </ogr:stats_by_category>
   </gml:featureMember>
   <gml:featureMember>
     <ogr:stats_by_category fid="stats_by_category.1">
       <ogr:id2>1</ogr:id2>
+      <ogr:count>2</ogr:count>
+      <ogr:unique>2</ogr:unique>
       <ogr:min>2</ogr:min>
       <ogr:max>5</ogr:max>
-      <ogr:mean>3.5</ogr:mean>
-      <ogr:stddev>2.12132034355964</ogr:stddev>
+      <ogr:range>3</ogr:range>
       <ogr:sum>7</ogr:sum>
-      <ogr:count>2</ogr:count>
+      <ogr:mean>3.5</ogr:mean>
+      <ogr:median>3.5</ogr:median>
+      <ogr:stddev>1.5</ogr:stddev>
+      <ogr:minority>2</ogr:minority>
+      <ogr:majority>2</ogr:majority>
+      <ogr:q1>2</ogr:q1>
+      <ogr:q3>5</ogr:q3>
+      <ogr:iqr>3</ogr:iqr>
     </ogr:stats_by_category>
   </gml:featureMember>
   <gml:featureMember>
     <ogr:stats_by_category fid="stats_by_category.2">
       <ogr:id2>0</ogr:id2>
+      <ogr:count>5</ogr:count>
+      <ogr:unique>5</ogr:unique>
       <ogr:min>3</ogr:min>
       <ogr:max>9</ogr:max>
-      <ogr:mean>6.6</ogr:mean>
-      <ogr:stddev>2.30217288664427</ogr:stddev>
+      <ogr:range>6</ogr:range>
       <ogr:sum>33</ogr:sum>
-      <ogr:count>5</ogr:count>
+      <ogr:mean>6.6</ogr:mean>
+      <ogr:median>7</ogr:median>
+      <ogr:stddev>2.0591260281974</ogr:stddev>
+      <ogr:minority>3</ogr:minority>
+      <ogr:majority>3</ogr:majority>
+      <ogr:q1>6</ogr:q1>
+      <ogr:q3>8</ogr:q3>
+      <ogr:iqr>2</ogr:iqr>
     </ogr:stats_by_category>
   </gml:featureMember>
 </ogr:FeatureCollection>
diff --git a/python/plugins/processing/tests/testdata/qgis_algorithm_tests.yaml b/python/plugins/processing/tests/testdata/qgis_algorithm_tests.yaml
index 0bcff7fcfa1..887813449e4 100644
--- a/python/plugins/processing/tests/testdata/qgis_algorithm_tests.yaml
+++ b/python/plugins/processing/tests/testdata/qgis_algorithm_tests.yaml
@@ -3476,3 +3476,98 @@ tests:
         name: expected/collect_two_fields.gml
         type: vector
 
+
+  - algorithm: qgis:statisticsbycategories
+    name: Stats by cat (float field)
+    params:
+      CATEGORIES_FIELD_NAME:
+      - name
+      INPUT:
+        name: dissolve_polys.gml
+        type: vector
+      VALUES_FIELD_NAME: floatval
+    results:
+      OUTPUT:
+        name: expected/stats_by_cat_float.gml
+        type: vector
+        pk: name
+        compare:
+          fields:
+            fid: skip
+
+  - algorithm: qgis:statisticsbycategories
+    name: Stats by cat (string field)
+    params:
+      CATEGORIES_FIELD_NAME:
+      - intval
+      INPUT:
+        name: dissolve_polys.gml
+        type: vector
+      VALUES_FIELD_NAME: name
+    results:
+      OUTPUT:
+        name: expected/stats_by_cat_string.gml
+        type: vector
+        pk: intval
+        compare:
+          fields:
+            fid: skip
+
+  - algorithm: qgis:statisticsbycategories
+    name: Stats by cat (two category fields)
+    params:
+      CATEGORIES_FIELD_NAME:
+      - intval
+      - name
+      INPUT:
+        name: dissolve_polys.gml
+        type: vector
+      VALUES_FIELD_NAME: floatval
+    results:
+      OUTPUT:
+        name: expected/stats_by_cat_two_fields.gml
+        type: vector
+        pk:
+          - intval
+          - name
+        compare:
+          fields:
+            fid: skip
+
+  - algorithm: qgis:statisticsbycategories
+    name: Stats by cat (no value field)
+    params:
+      CATEGORIES_FIELD_NAME:
+      - intval
+      - name
+      INPUT:
+        name: dissolve_polys.gml
+        type: vector
+    results:
+      OUTPUT:
+        name: expected/stats_by_cat_no_value.gml
+        type: vector
+        pk:
+          - intval
+          - name
+        compare:
+          fields:
+            fid: skip
+
+  - algorithm: qgis:statisticsbycategories
+    name: Stats by cat (date field)
+    params:
+      CATEGORIES_FIELD_NAME:
+      - date
+      INPUT:
+        name: custom/datetimes.tab
+        type: vector
+      VALUES_FIELD_NAME: date
+    results:
+      OUTPUT:
+        name: expected/stats_by_cat_date.gml
+        type: vector
+        pk: date
+        compare:
+          fields:
+            fid: skip
\ No newline at end of file
diff --git a/python/testing/__init__.py b/python/testing/__init__.py
index 7b8359de5ee..4cea7c414cf 100644
--- a/python/testing/__init__.py
+++ b/python/testing/__init__.py
@@ -105,7 +105,11 @@ class TestCase(_TestCase):
 
         def sort_by_pk_or_fid(f):
             if 'pk' in kwargs and kwargs['pk'] is not None:
-                return f[kwargs['pk']]
+                key = kwargs['pk']
+                if isinstance(key, list) or isinstance(key, tuple):
+                    return [f[k] for k in key]
+                else:
+                    return f[kwargs['pk']]
             else:
                 return f.id()
 
diff --git a/src/core/processing/qgsprocessingparameters.cpp b/src/core/processing/qgsprocessingparameters.cpp
index 59561855195..ac1265060a6 100644
--- a/src/core/processing/qgsprocessingparameters.cpp
+++ b/src/core/processing/qgsprocessingparameters.cpp
@@ -2301,6 +2301,9 @@ bool QgsProcessingParameterField::checkValueIsAcceptable( const QVariant &input,
   {
     if ( !mAllowMultiple )
       return false;
+
+    if ( input.toList().isEmpty() && !( mFlags & FlagOptional ) )
+      return false;
   }
   else if ( input.type() == QVariant::String )
   {
diff --git a/tests/src/core/testqgsprocessing.cpp b/tests/src/core/testqgsprocessing.cpp
index de11fe2c9cc..0bc2c122043 100644
--- a/tests/src/core/testqgsprocessing.cpp
+++ b/tests/src/core/testqgsprocessing.cpp
@@ -2258,6 +2258,8 @@ void TestQgsProcessing::parameterLayerList()
   QVERIFY( !def->checkValueIsAcceptable( true ) );
   QVERIFY( !def->checkValueIsAcceptable( 5 ) );
   QVERIFY( !def->checkValueIsAcceptable( "layer12312312" ) );
+  QVERIFY( !def->checkValueIsAcceptable( QVariantList() ) );
+  QVERIFY( !def->checkValueIsAcceptable( QStringList() ) );
   QVERIFY( def->checkValueIsAcceptable( QStringList() << "layer12312312" << "layerB" ) );
   QVERIFY( def->checkValueIsAcceptable( QVariantList() << "layer12312312" << "layerB" ) );
   QVERIFY( !def->checkValueIsAcceptable( "" ) );
@@ -3183,6 +3185,8 @@ void TestQgsProcessing::parameterField()
   QVERIFY( def->checkValueIsAcceptable( QVariantList() << "a" << "b" ) );
   QVERIFY( !def->checkValueIsAcceptable( "" ) );
   QVERIFY( !def->checkValueIsAcceptable( QVariant() ) );
+  QVERIFY( !def->checkValueIsAcceptable( QStringList() ) );
+  QVERIFY( !def->checkValueIsAcceptable( QVariantList() ) );
 
   params.insert( "non_optional", QString( "a;b" ) );
   fields = QgsProcessingParameters::parameterAsFields( def.get(), params, context );