Calculate the range, population variance, and population standard deviation for the following data set. If necessary, round to o

Question

3 years ago

6

ne more decimal place than the largest
number of decimal places given in the data.
6,9,9,6,9, 4, 8, 5, 8, 27
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1 answer:

Len [333] · Answer 1 · 2022-12-17T21:23:45+03:00

The standard deviation of a sample is the square root of the variance

<h3>How to calculate the range</h3>

From the dataset, the smallest is 4 and the highest is 27

So, the range is:

$Range = 27 - 4$

$Range = 23$

Hence, the range is 23

<h3>How to determine the variance</h3>

The sample is given as: 6,9,9,6,9, 4, 8, 5, 8, 27

Start by calculating the mean

$\bar x = \frac{\sum x}{n}$

So, we have:

$\bar x = \frac{6+9+9+6+9+ 4+ 8+ 5+ 8+ 27}{10}$

$\bar x = \frac{91}{10}$

$\bar x = 9.1$

The population variance is then calculated as:

$\sigma^2 = \frac{\sum(x - \bar x)^2}{n }$

This gives

$\sigma^2 = \frac{(6 - 9.1)^2+(9- 9.1)^2+(9- 9.1)^2+(6- 9.1)^2+(9- 9.1)^2+(4- 9.1)^2+(8- 9.1)^2+(5- 9.1)^2+(8- 9.1)^2+(27- 9.1)^2}{10}$

$\sigma^2 = 38.49$

Hence, the population variance is 5.5

<h3>How to calculate the standard deviation</h3>

In (a), we have:

$\sigma^2 = 38.49$

Take the square roots of both sides

$\sigma = 6.20$

Hence, the population standard deviation is 6.20

Read more about variance and standard deviation at: