Weighted Average Standard Deviation

[kthenning]

I'm doing a customer survey where people have responded:

Agree strongly 331
Agree somewhat 100
Neither 50
Disagree somewhat 10
Disagree strongly 5

I want to assign a 1 to 5 score to each response (1=agree strongly) and get
the weighted average standard deviation using just the frequencys above. Is
this possible in Excel? If so, what would the equation be? I saw another
post about a wmean, wsd...but the equation returns a !NAME error.
Please help...Thank you

 

[joeu2004]

I'm doing a customer survey where people have responded:
Agree strongly 331
Agree somewhat 100
Neither 50
Disagree somewhat 10
Disagree strongly 5
I want to assign a 1 to 5 score to each response (1=agree strongly)
and get the weighted average standard deviation [...].
Is this possible in Excel?

There might be an easier way, but the following works,
and it straight-forwardly follows the math definitions.

Assume that A1:A5 has the values above, and B1:B5 has
the respective scores. Then the average score (C1) is:

=SUMPRODUCT(A1:A5,B1:B5)/(SUM(A1:A5)-1)

and the variance (C2) of the scores is:

=SUMPRODUCT(A1:A5,(B1:B5-C1)^2)/(SUM(A1:A5)-1)

The standard deviation is simply the square root of
the variance, namely:

=SQRT(C2)

Note: The formulas assume that you want to treat the
responses as samples. For the population average and
variance, remove "-1" in the denominator.

 

[kthenning]

Thank you!!

I'm doing a customer survey where people have responded:
Agree strongly 331
Agree somewhat 100
Neither 50
Disagree somewhat 10
Disagree strongly 5
I want to assign a 1 to 5 score to each response (1=agree strongly)
and get the weighted average standard deviation [...].
Is this possible in Excel?

There might be an easier way, but the following works,
and it straight-forwardly follows the math definitions.

Assume that A1:A5 has the values above, and B1:B5 has
the respective scores. Then the average score (C1) is:

=SUMPRODUCT(A1:A5,B1:B5)/(SUM(A1:A5)-1)

and the variance (C2) of the scores is:

=SUMPRODUCT(A1:A5,(B1:B5-C1)^2)/(SUM(A1:A5)-1)

The standard deviation is simply the square root of
the variance, namely:

=SQRT(C2)

Note: The formulas assume that you want to treat the
responses as samples. For the population average and
variance, remove "-1" in the denominator.

 

[Jerry W. Lewis]

(e-mail address removed) wrote:

....

Assume that A1:A5 has the values above, and B1:B5 has
the respective scores. Then the average score (C1) is:

=SUMPRODUCT(A1:A5,B1:B5)/(SUM(A1:A5)-1)

I think you meant

=SUMPRODUCT(A1:A5,B1:B5)/SUM(A1:A5)

Jerry

 

[joeu2004]

I think you meant
=SUMPRODUCT(A1:A5,B1:B5)/SUM(A1:A5)

Yes, you are right. Overzealous editing. Only the
variance formula changes for sample v. population
statistics.