Question

A population of small bottles and their contents has the following weights (in grams): 4, 2, 5, 4, 5, 2, and 6. What is the variance of bottle weight?

A. 6.92.
B. 4.80.
C. 1.96.
D. 2.33.

Answer 1

D. 2.33.

Explanation:

Given;

the weight distribution of the bottles = 4, 2, 5, 4, 5, 2, and 6

sum of the weights = 28

the mean (x) = 28/7

x = 4

the sum of square of the mean deviation is calculated as:

= (4 - 4)² + (2 - 4)² + (5 - 4)² + (4 - 4)² + (5 - 4)² + (2 - 4)² + (6 - 4)²

= 0 + 4 + 1 + 0 + 1 + 4 + 4

= 14

`the \ variance \ is \ calculated \ as:\\\\\sigma ^2 = (\sum (x-\bar x)^2)/(n-1) \\\\\sigma ^2 = (14)/(7-1) = (14)/(6) = 2.33`

Therefore, the correct answer is D