Chapter 2.2, Problem 2.36E

(a)

To determine

To Calculate: the mean and explain it.

Answer to Problem 2.36E

  $\mu =8$

Explanation of Solution

Given:

Students sleep hours

7  7  9  9

Formula used:

  $\mu =\frac{{\displaystyle \sum x}}{n}$

Calculation:

  $\begin{array}{c}\mu =\frac{{\displaystyle \sum x}}{n}\\ =\frac{7+7+9+9}{4}\\ =\frac{32}{4}\\ \mu =8\end{array}$

. On the basis of given data sleep of hours of four students, calculating the mean which is sum of all values divided by the number of values which is 8. It shows that on average reply were 8 and they slept on average 8 hours last night.

(b)

To determine

To Calculate: the deviation of each observation from the mean and evaluate the standard deviation and explain it

Answer to Problem 2.36E

  $\sigma =1.55$

Explanation of Solution

Given:

Seven person’s metabolic rates

1792 1666 1362 1614 1460 1867 1439

Formula used:

  $\sigma =\sqrt{\frac{{\displaystyle \sum {(x-\overline{x})}^2}}{n-1}}$

Calculation:

$x$	$x-\overline{x}$	${(x-\overline{x})}^2$
7	-1	1
7	-1	1
9	1	1
9	1	1
		4

  ${\displaystyle \sum {(x-\overline{x})}^2}=4$

  $\begin{array}{c}\sigma =\sqrt{\frac{{\displaystyle \sum {(x-\overline{x})}^2}}{n-1}}\\ =\sqrt{\frac{4}{4-1}}\\ \approx 1.55\end{array}$

As calculated mean and standard deviation are 8 and 1.55 respectively. It is showing that the standard deviation 8 is about to 1.55 which means that almost people sleep between about 6.5 and about 9.5 hours.