Question

1.) Find the population variance and standard deviation for the following population. Round the answers to at least two decimal places.

19 9 18 8 28 29

The population variance is. _____

The population standard deviation is ______

2.) Find the sample variance and standard deviation for the following sample. Round the answers to two decimal places as needed.

17

33

23

16

13

The sample variance is ______

The sample standard deviation is ______

Answer 1

Before calculation, let us make sure what is difference between sample and population variance

1. To find variance we first need to find mean

Create the following table.

data	data-mean	(data - mean)2
19	0.5	0.25
9	-9.5	90.25
18	-0.5	0.25
8	-10.5	110.25
28	9.5	90.25
29	10.5	110.25

Find the sum of numbers in the last column to get.

So population variance is

So population standard deviation is

2. Now mean for this case is

Create the following table.

data	data-mean	(data - mean)2
17	-3.4	11.56
33	12.6	158.76
23	2.6	6.76
16	-4.4	19.36
13	-7.4	54.76

Find the sum of numbers in the last column to get.

So sample variance

So sample standard deviation is