Question

the numbers of regular season wins for 10 football teams in a given season are given below. determine the range, mean, variance, and standard deviation of the population data set.

2, 10, 15, 2, 12, 10, 12, 8, 4, 8

the range is 13.
(simplify your answer.)

the population mean is 8.3.
(simplify your answer. round to the nearest tenth as needed.)

the population variance is 17.6.
(simplify your answer. round to the nearest tenth as needed.)

the population standard deviation is .
(simplify your answer. round to the nearest tenth as needed.)

Explanation:

Identify the given data and parameters

We are given a population dataset representing the number of regular season wins for \(N = 10\) football teams:

$$ 2, 10, 15, 2, 12, 10, 12, 8, 4, 8 $$

We need to find the population standard deviation, given that:

• The range is \(13\)
• The population mean \(\mu\) is \(8.3\)
• The population variance \(\sigma^2\) is \(17.6\)

Calculate the population standard deviation

Using the Population Standard Deviation and Population Variance knowledge points

$$ \sigma = \sqrt{\sigma^2} = \sqrt{17.6} \approx 4.1952 $$

Round to the nearest tenth

Using the Population Standard Deviation knowledge point

$$ \sigma \approx 4.2 $$

Answer:

The population standard deviation is <blank>\(4.2\)</blank>