Question

You have found the following ages (in years) of all 666 lions at your local zoo: 13,2,1,5,2,7 What is the average age of the lions at your zoo? What is the standard deviation? Average age: _____ years old Standard deviation: ____ years

Answer 1

Answer:

$Mean = 5$

$S_x = 4.123$

Step-by-step explanation:

Given

Number of Lions, n: 6

Ages: 13, 2, 1, 5, 2, 7

Required

Determine the:

1. Mean

2. Standard Deviation

Mean is calculated as;

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

$Mean = \frac{13+2+1+5+2+7}{6}$

$Mean = \frac{30}{6}$

$Mean = 5$

Standard Deviation is calculated as follows

$S_x = \sqrt{\frac{\sum (x_i - Mx)^2}{N}}$

Where Mx represent mean

Substitute values for x, Mean and Land

$S_x = \sqrt{\frac{(13 - 5)^2+(2 - 5)^2+(1 - 5)^2+(5 - 5)^2+(2 - 5)^2+(7 - 5)^2}{6}}$

$S_x = \sqrt{\frac{(8)^2+(- 3)^2+(-4)^2+(0)^2+(-3)^2+(2)^2}{6}}$

$S_x = \sqrt\frac{64+9+16+0+9+4}{6}}$

$S_x = \sqrt\frac{102}{6}}$

$S_x = \sqrt{17}$

$S_x = 4.123$

The mean and standard deviation is 5 and 4.123 respectively