Question

Consider the following sets of sample data: A: $36,700, $30,300, $22,800, $27,700, $37,700, $39,800, $27,000, $30,100, $33,900, $24,900, $27,500, $37,600, $32,700, $34,200 B: 21,253, 21,065, 20,747, 21,905, 20,546, 21,580, 22,292, 20,072, 20,518, 20,426, 20,839 Step 1 of 2 : For each of the above sets of sample data, calculate the coefficient of variation, CV. Round to one decimal place.

Answer 1

Answer:

16.6% ; 3.2%

Step-by-step explanation:

Given the data :

Data A:

$36,700, $30,300, $22,800, $27,700, $37,700, $39,800, $27,000, $30,100, $33,900, $24,900, $27,500, $37,600, $32,700, $34,200

Data B: 21,253, 21,065, 20,747, 21,905, 20,546, 21,580, 22,292, 20,072, 20,518, 20,426, 20,839

The Coefficient of variation (CV) = (Sample standard deviation / Sample mean)

Sample mean (m) ;

Σx / n

n = sample size

Sample standard deviation (S) :

√[(x - m)² / (n-1)]

To save computation time ;

The sample mean and sample standard deviation can be obtained using a calculator :

For Data A:

Sample mean (m) = 31635.7143

Sample Standard deviation (s) = 5256.14763

Hence, Coefficient of variation :

5256.14763 / 31635.7143

= 0.166

= 0.166 * 100% = 16.6%

For Data B:

Sample mean (m) = 21022.0909

Sample Standard deviation (s) = 678.718271

678.718271 / 21022.0909

= 0.032

= 0.032 * 100% = 3.2%