Question

A sample of small bottles and their contents has the following weights (in grams): 4,1,5,4,5,7, and 6. What is the sample variance of bottle weight?

Answer 1

3.62

Explanation:

The formula for sample variance is:

`s^2=(1)/(n-1) \Sigma (x_i - \bar x)^2`

Where s^2 denotes variance

n is the number of numbers (here it is 7)

x_i are all the individual values

x_bar is the mean(average)

First, let's calculate mean:

(4+1+5+4+5+7+6)/7 = 32/7 = 4.57

Now, the variance:

`((4-4.57)^2 + (1-4.57)^2 +(5-4.57)^2 + (4-4.57)^2 + (5-4.57)^2 + (7-4.57)^2 + (6-4.57)^2)/(7-1)\\=3.62`

The sample variance of bottle weight is 3.62