Question

Twenty-five randomly selected students were asked the number of movies they watched the previous week. The results are as follows. # of movies Frequency 0 5 1 9 2 5 3 5 4 1 (a) Find the sample mean x. (Enter your answer to two decimal places.) x = (b) Find the approximate sample standard deviation, s. (Round your answer to two decimal places.) s =

Answer 1

a) x = 1.52

b) s = 1.16

Explanation:

We have that:

5 students watched 0 movies.

9 students watched 1 movie.

5 students watched 2 movies.

5 students watched 3 movies.

1 student watched 4 movies.

(a) Find the sample mean x.

Sum divided by the number of students. So

`x = (5*0 + 9*1 + 5*2 + 5*3 + 1*4)/(5 + 9 + 5 + 5 + 1) = (38)/(25) = 1.52`

(b) Find the approximate sample standard deviation, s.

Standard deviation of the sample.

Square root of the sum of the squares of the values subtracted from the mean, divided by the sample size subtracted by 1. So

`s = \sqrt{(5*(0-1.52)^2 + 9*(1-1.52)^2 + 5*(2-1.52)^2 + 5*(3-1.52)^2 + 1*(4-1.52)^2)/(24)} = \sqrt{(32.24)/(24)} = 1.16`