Calculate Weighted Average and Weighted Standard Deviation in DAX - powerbi

Question

This is something I have never attempted before
I want to calculate the weighted standard deviation and the weighted average for the dataset containing records for actual values measured against set values
The calculation is to be done using a DAX query in PowerBI
Set Value 1
Actual Value 1
Set Value 2
Actual Value 2
10
8
101
102
10
11
101
104
10
12
101
97
10
7
101
99
10
13
101
97
10
13
101
100
10
9
101
98
10
10
101
100
10
8
101
102
10
14
101
98
10
8
101
98
10
13
101
96
10
13
101
103
10
14
101
102
10
7
202
205
20
18
202
198
20
18
202
197
20
19
202
203
20
19
202
202
20
19
202
201
20
22
202
202
20
18
202
200
20
17
202
195
20
23
202
198
Edit 1:
Please use the data above.
Also, please note that although, set points are what we intend to use as weights but its the count of a particular set point. for eg: if the setpoint1 10 is repeating 15 times and set point1 20 is repeating 9 times then wieght to be used as 15 & 9 respectively

Answer 1

Weighted Average and Standard deviation can be implemented in DAX according to their mathematical definition.
Assuming we have a table with the columns Weight and Value the formula for the Weighted Average is
WAvg =
VAR Num = SUMX( Samples, Samples[Weight] * Samples[Value] )
VAR Den = SUM( Samples[Weight] )
RETURN DIVIDE( Num, Den )
and the formula for the Weighted Standard Deviation is
WStdDev =
VAR WAvg = [WAvg]
VAR Num = SUMX( Samples, Samples[Weight] * (Samples[Value] - Wavg)^2 )
VAR Den = SUM( Samples[Weight] )
VAR WVar = DIVIDE( Num, Den )
RETURN SQRT(WVar)
Edit:
if I understand your new request, the Weight is the number of rows with the same Set Value, that is to be used for each of the Actual Value. Then, since there are two pairs of columns, I assume that the requirement is to have a set of measures per each couple of columns.
The formula requires to add a count of the number of rows per each group of Set Value, to be used as weight. I imported the sample table as table "V"
Weighted average for Set Value 1 and Actual Value 1
WAvg1 =
VAR Num =
SUMX(
ALL( V ),
CALCULATE( COUNTROWS( V ), ALLEXCEPT( V, V[Set Value 1] ) ) * V[Actual Value 1]
)
VAR Den =
SUMX(
ALL( V ),
CALCULATE( COUNTROWS( V ), ALLEXCEPT( V, V[Set Value 1] ) )
)
RETURN
DIVIDE( Num, Den )
Weighted average for Set Value 2 and Actual Value 2
WAvg2 =
VAR Num =
SUMX(
ALL( V ),
CALCULATE( COUNTROWS( V ), ALLEXCEPT( V, V[Set Value 2] ) ) * V[Actual Value 2]
)
VAR Den =
SUMX(
ALL( V ),
CALCULATE( COUNTROWS( V ), ALLEXCEPT( V, V[Set Value 2] ) )
)
RETURN
DIVIDE( Num, Den )
Weighted standard deviation for Set Value 1 and Actual Value 1
WStdDev1 =
VAR Num =
SUMX(
ALL( V ),
VAR WAvg = [WAvg1]
RETURN
CALCULATE( COUNTROWS( V ), ALLEXCEPT( V, V[Set Value 1] ) ) * ( V[Actual Value 1] - WAvg ) ^ 2
)
VAR Den =
SUMX(
ALL( V ),
CALCULATE( COUNTROWS( V ), ALLEXCEPT( V, V[Set Value 1] ) )
)
VAR WVariance =
DIVIDE( Num, Den )
RETURN
SQRT( WVariance )
Weighted standard deviation for Set Value 2 and Actual Value 2
WStdDev2 =
VAR Num =
SUMX(
ALL( V ),
VAR WAvg = [WAvg2]
RETURN
CALCULATE( COUNTROWS( V ), ALLEXCEPT( V, V[Set Value 2] ) ) * ( V[Actual Value 2] - WAvg ) ^ 2
)
VAR Den =
SUMX(
ALL( V ),
CALCULATE( COUNTROWS( V ), ALLEXCEPT( V, V[Set Value 2] ) )
)
VAR WVariance =
DIVIDE( Num, Den )
RETURN
SQRT( WVariance )
Applying these formulas to the sample table we get these results