Calculate the range, population variance, and population standard deviation for the following data set. If necessary, round to one more decimal place than the largest number of …

Question

asked Sep 22, 2022 188k views

1 Answer

Jorge Granados · Answer 1 · 2022-09-27T02:15:59+0000

Answer:

Range = 11

$\sigma^2 = 12.1$

$\sigma = 3.5$

Explanation:

Given

Data: 16,12,17,8,15,15,10,11,19,18

Solving (a): Range

This is calculated as:

Range = Highest - Least

Where:

Highest = 19

Least = 8

So:

Range = 19 - 8

Range = 11

Solving (b): The population variance

First, calculate the population mean using:

$\mu = (\sum x)/(n)$

So:

$\mu = (16+12+17+8+15+15+10+11+19+18)/(10)$

$\mu = (141)/(10)$

$\mu = 14.1$

So, the population variance is:

$\sigma^2 = (\sum(x - \mu)^2)/(n)$

$\sigma^2 = ((16 - 14.1)^2 + (12 - 14.1)^2 +............... + (19- 14.1)^2 + (18- 14.1)^2)/(10)$

$\sigma^2 = (120.9)/(10)$

$\sigma^2 = 12.09$

$\sigma^2 = 12.1$ --- approximated

Solving (c): The population standard deviation.

This is calculated as:

$\sigma = \sqrt{\sigma^2$

$\sigma = \sqrt{12.09$

$\sigma = 3.5$