Standard Deviation

Standard deviation shows the variation from your data. Here is a math problem to give an example of how to find standard deviation based on collected data.

Seven students on an intramural team weigh 148 lb, 155 lb, 143 lb, 154 lb, 145 lb, 164 lb and 141 lb. What is the standard deviation of the weight of these students.

1) Find the mean.
 148+155+143+154+145+164+141       = 150
                       7
2) Subtract the mean from each of the weights.
148-150 = -2
155-150 = 5
143-150 = -7
154-150 = 4
145-150 = -5
164-150 = 14
141-150 = -9

3) Square each of the differences from step 2.
(-2)^2 = 4
(5)^2 = 25
(-7)^2=49
(4)^2 = 16
(-5)^2 = 25
(14)^2 = 196
(-9)^2 = 81

4) Add up all your answers from step 3.
4+25+49+16+25+196+81 = 396

5)Divide the sum from step 4 by the number of weights to get the variance.
396   =56.571
 7

6) Square the answer from step 5 to find the standard deviation.
56.571 = 7.5
 7

Your standard deviation is 7.5