Question 259798
This is how I answered a similar problem. The numbers are different but the theory is the same.


D = Data | M = Midpoint = x | F = Frequency

D      |     F	  |    M            |      (X * F): |   (X^2*F)
0-7   |      4    |  (0+7)/2 = 3.5         |   3.5*4 = 14  |(3.5^2*4) = 49
8-15   |     2    |  (8+15)/2 = 11.5     |   11.5*2 = 23  |    (11.5^2*2) =264.5
16-23   |     1    |  (16+23)/2 = 19.5  |   19.5*1 = 19.5 |(19.5^2*1) =380.25
24-31   |     2    |  (24+31)/2 = 27.5  |   27.5*2 = 55   |  (27.5^2*2) =1512.5
32-39   |     1    |  (32+39)/2 = 35.5  |   35.5*1 = 35.5  | (35.5^2*1) =1260.25
40-47   |     4    |  (40+47)/2 = 43.5  |   43.5*4 =174	    | (43.5^2*4)=7569
SUM:   |     14    |  141               |	321        |   11060.25

Mean (x-bar) = 321/14 = 22.9 = 23


**********

Variance:
S^2 = [11060.25-(321^2/14)]/(14-1)
S^2 = [11060.25-(7360.07)]/(13)
S^2 = 3700.18/13
Variance = 284.63

**********

Standard Dev.
S^2= 284.63
S = sqrt284.63
Standard Dev. = 16.87