Question

Consider the following sets of sample data:

A: $31,100$⁢31,100, $25,800$⁢25,800, $36,300$⁢36,300, $30,200$⁢30,200, $30,000$⁢30,000, $19,800$⁢19,800, $22,300$⁢22,300, $22,600$⁢22,600, $34,900$⁢34,900, $21,700$⁢21,700, $36,900$⁢36,900, $30,800$⁢30,800, $31,700$⁢31,700, $37,100$⁢37,100

B: 3.183.18, 4.244.24, 4.274.27, 4.384.38, 3.873.87, 4.754.75, 3.433.43, 3.353.35, 4.164.16, 4.814.81, 2.982.98

For each of the above sets of sample data, calculate the coefficient of variation, CV. Round to one decimal place.

Answer 1

For Set A

Mean value is

Create the following table.

data	data-mean	(data - mean)2
31100	1728.5714	2987959.084898
25800	-3571.4286	12755102.244898
36300	6928.5714	48005101.644898
30200	828.5714	686530.56489796
30000	628.5714	395102.00489796
19800	-9571.4286	91612245.444898
22300	-7071.4286	50005102.444898
22600	-6771.4286	45852245.284898
34900	5528.5714	30565101.724898
21700	-7671.4286	58850816.764898
36900	7528.5714	56679387.324898
30800	1428.5714	2040816.244898
31700	2328.5714	5422244.764898
37100	7728.5714	59730815.884898

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

So standard deviation is

So coefficient of variation is

Now for set B

Sample mean is

Create the following table.

data	data-mean	(data - mean)2
3.18	-0.7673	0.58874929
4.24	0.2927	0.08567329
4.27	0.3227	0.10413529
4.38	0.4327	0.18722929
3.87	-0.0773	0.00597529
4.75	0.8027	0.64432729
3.43	-0.5173	0.26759929
3.35	-0.5973	0.35676729
4.16	0.2127	0.04524129
4.81	0.8627	0.74425129
2.98	-0.9673	0.93566929

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

So standard deviation is

So CV is