Chapter 2.2, Problem 2.50E

(a)

To determine

To Calculate: the mean on the basis of given data.

Answer to Problem 2.50E

  $\mu =5.4$

Explanation of Solution

Given:

5.6 5.2 4.6 4.9 5.7 6.4

Formula used:

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

Calculation:

  $\begin{array}{c}\mu =\frac{{\displaystyle \sum x}}{n}\\ =\frac{5.6+5.2+4.6+4.9+5.7+6.4}{6}\\ =\frac{32.4}{6}\\ =5.4\end{array}$

(b)

To determine

To Calculate: the standard deviation.

Answer to Problem 2.50E

  $\sigma =0.64$

Explanation of Solution

Given:

5.6 5.2 4.6 4.9 5.7 6.4

Formula used:

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

Calculation:

$x$	$x-\overline{x}$	${\left(x-\overline{x}\right)}^2$
5.6	0.2	0.04
5.2	-0.2	0.04
4.6	-0.8	0.64
4.9	-0.5	0.25
5.7	0.3	0.09
6.4	1	1
		2.06

  ${{\displaystyle \sum \left(x-\overline{x}\right)}}^2=2.06$

  $\begin{array}{c}\sigma =\sqrt{\frac{{{\displaystyle \sum \left(x-\overline{x}\right)}}^2}{n-1}}\\ =\sqrt{\frac{2.06}{6-1}}\\ \approx 0.64\end{array}$

(c)

To determine

To Explain: that for the hand calculation are you agree or not which using calculator to obtain mean and standard deviation.

Answer to Problem 2.50E

Yes, agree

  $\mu =5.4$

  $\sigma =0.64$

Explanation of Solution

Yes, agree by the hand calculation of mean and standard deviation because it is giving the same result by the calculator also in which enter the same data.