How to Calculate Standard D

[Kevin Neufeld]

I have a sample table below. It represents model sizes of products, that are measured in Feet. the sales quantity is the number of each model sized sold. I am wanting to know the Avg Size sold. So I used a weighted average. I also wanted to know the standard deviation of size sold. I have shown below in green, blue and red the end results of the 3 metrics I wanted. Below each I have the steps / formulas used to obtain each. Just wanted to confirm with this group I did this correct.

Thanks in Advance.

Model Size (Feet)	Sales Quantity
12	1
15	15
18	40
21	139
24	237
27	179
30	569
33	119
36	1057
39	4
42	764
48	1073
54	98
60	261
66	0
72	65
75	14
78	52
90	45
105	82
135	6
156	0
Total	4820
Formula used for Total	=SUM(B2:B23)
Avg Size (wgt'd)	41.8
Formula used for - Avg Size (wgt'd)	=SUMPRODUCT($A$2:$A$23,B2:B23)/SUM(B2:B23)
Standard Deviation	15.1
Steps used for Standard Deviation
Step 1	=B2*A2+A3*B3+A4*B4+A5*B5+A6*B6+A7*B7+A8*B8+A9*B9+A10*B10+A11*B11+A12*B12+A13*B13+A14*B14+A15*B15+A16*B16+A17*B17+A18*B18+A19*B19+A20*B20+A21*B21+A22*B22+A23*B23
Step 2	=(B2*A2)*A2+(B3*A3)*A3+(B4*A4)*A4+(B5*A5)*A5+(B6*A6)*A6+(B7*A7)*A7+(B8*A8)*A8+(B9*A9)*A9+(B10*A10)*A10+(B11*A11)*A11+(B12*A12)*A12+(B13*A13)*A13+(B14*A14)*A14+(B15*A15)*A15+(B16*A16)*A16+(B17*A17)*A17+(B18*A18)*A18+(B19*A19)*A19
Step 3	=B30/B25
Step 4	=((B25*B31)-(B30^2))/((B25*(B25-1)))
Step 5	=SQRT(B33)

 

[Sulprobil]

Hello,

I did not check your formulas but I think that your results are correct.
I calculated:
Weighted Average: 41.7846473
Weighted STDEV: 15.12314028
Weighted Variance: 228.709372

Regards,
Bernd