Question

We are going to calculate the standard deviation for the following set of sample data.

1) First, calculate the mean.
¯x=x¯=

2) Fill in the table below. Fill in the differences of each data value from the mean, then the squared differences.
3) Calculate the standard deviation.

xxx−¯xx-x¯(x−¯x)2(x-x¯)2

14

4

4

14

5

Total

Answer 1

1) sample size (n) = 5

Sample mean is,

2)

x
14	(14 - 8.2) = 5.8	(5.8)2 = 33.64
4	(4 - 8.2) = -4.2	(-4.2)2= 17.64
4	(4 - 8.2) = -4.2	(-4.2)2 = 17.64
14	(14 - 8.2) = 5.8	(5.8)2 = 33.64
5	(5 - 8.2) = -3.2	(-3.2)2 = 10.24

3) Sample standard deviations is,

=> Sample standard deviation = 5.3104

And population standard deviation is,

=> Population standard deviation = 4.7497