SOLUTION: Can someone please put me on the right track i ask this question four time and no answer was given. You are given the following frequency distribution for the number of errors

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Question 259798: Can someone please put me on the right track i ask this question four time and no answer was given.

You are given the following frequency distribution for the number of errors that students made in a test
Errors Frequency
0-2 14
3-5 1
6-8 9
9-11 19
12-14 17
Find the mean, variance, and the standard deviation
please help ASAP!!!!!!!!!!!!!!!!!
Found 2 solutions by richwmiller, dylantc77:
Answer by richwmiller(17219) (Show Source):
You can put this solution on YOUR website!
This is not my field but here is something that might help.
http://davidmlane.com/EXCEL/standard_deviation.html

Answer by dylantc77(3) (Show Source):
You can put this solution on YOUR website!
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