Chapter 2.2, Problem 2.34E

(a)

To determine

To Calculate: the deviation of each observation from the mean and show that the sum of the deviations is 0.

Explanation of Solution

Given:

Seven person’s metabolic rates

1792 1666 1362 1614 1460 1867 1439

Calculation:

$x$	$x-\overline{x}$
1792	192
1666	66
1362	-238
1614	14
1460	-140
1867	267
1439	-161

Sum of the deviations from the mean should be 0

=192+66-238+14-140+267-161

=0

(b)

To determine

To Calculate: the standard deviation.

Answer to Problem 2.34E

  $\sigma =189.24$

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:

$x$	$x-\overline{x}$	${(x-\overline{x})}^2$
1792	192	36864
1666	66	4356
1362	-238	56644
1614	14	196
1460	-140	19600
1867	267	71289
1439	-161	25921
		214872

  ${\displaystyle \sum {(x-\overline{x})}^2}=214870$

  $\begin{array}{c}\sigma =\sqrt{\frac{{\displaystyle \sum {(x-\overline{x})}^2}}{n-1}}\\ =\sqrt{\frac{214870}{7-1}}\\ \approx 189.24\end{array}$

The standard deviation about to mean is 189.24