Question

If a sample of 51 employees were taken from a population of 606 employees. s² could refer to the variance of how many employees salaries?

A. 606
B. Both 51 and 606
C. Neither 51 or 606
D. 51

Answer 1

Variance measures how variate in the data set is spread from mean and from other variates in data set.

Variance(s²), is calculated by difference between each number in the data set and the mean,and then squaring the result, and then dividing the sum of the squares of each variate in the new data set by total number of variate in new data set.

Now coming to the Question

Total Population=606

Sample Size chosen for employee salary=51

Since, sample size

`=(51)/(606)* 100\\\\=(5100)/(606)\\\\=8.42`Percent

Sample size is too small that is only , 8.42 % of total data set.

So, it would refer to variance of only 51, employees salaries.

Option D--51

Answer 2

In calculating for the variance, we use the actual sample size and not the population size. In this case since we are only using a sample size of 51 employees, then s^2 or sample variance refers to the variance of 51 employees.

Therefore the answer is letter D. 51