multiply the midpoint of each class by the frequency.

Do this for all 5 classes. Total the 5 products and divide by n.

2.5 * 2 = 5

7.5 * 7 = 52.5

12.5 * 12 = 150

17.5 * 6 = 105

22.5 * 3 = 67.5

Total = 380

n = 2 + 7 + 12 + 6 + 3 = 30

Mean = 380 / 30 = 12.6666

To find the standard deviation:

1) Subtract the mean from the class midpoint. That is, find (M – xbar). For the first class (2.5 – 12.6666 = -10.1666), for the second class (7.5 – 12.6666 = -5.1666), etc.

2) Square the difference between the class midpoint and the mean. For the first class it would be (-10.1666^2 = 103.36), for the second class (-5.1666^2 = 26.69), etc.

3) Multiply the squared difference between the class midpoint and the mean by the class frequency. For the first class the value is 2*(2.5 – 12.6666)^2 = 206.72. For the second class the value is 7*(7.5 – 12.6666)^2 = 186.86, and so on.

4) Add all the results from Step 3. The total is 824.1667.

s = sqrt [824.1667 / (30 – 1)] = 5.331

I’ve uploaded an Excel spreadsheet of the problem at:

http://i12.tinypic.com/4tr0j9c.jpg

or you can pay $3.34 for the solution at:

http://www.brainmass.com/homework-help/statistics/all-topics/93131

Good luck in your studies,

~ Mitch ~

http://www.ltcconline.net/greenl/java/Statistics/FrequencyData/FrequencyData.html