Chapter 3, Problem 1PP

(a)

To determine

To find: The sample size.

Explanation of Solution

Given:

The data set is:

112
128
108
129
125
153
155
132
137

The provided data represents that there are total 9 observations. Thus, the sample size is 9.

(b)

To determine

To find: The sum of the provided observations.

Answer to Problem 1PP

The sum is 1179.

Explanation of Solution

The sum of the provided observations can be calculated as:

  $\begin{array}{c}\text{Sum of observations}=112+128+\mathrm{....}+137\\ =1179\end{array}$

Thus, the required sum is 1179.

(c)

To determine

To fin: The mean of the provided observation and apply the units after calculation.

Answer to Problem 1PP

The mean is 131 mm Hg

Explanation of Solution

The mean for the provided data set can be computed as:

  $\begin{array}{c}\text{Mean}=\frac{\text{Sum of observations}}{\text{Number of observations}}\\ =\frac{1179}{9}\\ =131\end{array}$

Thus, the mean is 131 mm Hg.

(d)

To determine

To find: The sum of square.

Answer to Problem 1PP

The value of the sum of square is 2036.

Explanation of Solution

The sum of square is computed as:

$x$	$\left(x-\overline{x}\right)$	${\left(x-\overline{x}\right)}^2$
112	-19	361
128	-3	9
108	-23	529
129	-2	4
125	-6	36
153	22	484
155	24	576
132	1	1
137	6	36
		${\displaystyle \sum {\left(x-\overline{x}\right)}^2}=2036$

Thus, the sum of square is 2036.

(e)

To determine

To find: The variance for the provided data set.

Answer to Problem 1PP

The variance is 254.2

Explanation of Solution

Variance for the provided data set is computed as:

  $\begin{array}{c}{s}^2=\frac{{\displaystyle \sum {\left(x-\overline{x}\right)}^2}=2036}{n-1}\\ =\frac{2036}{9-1}\\ =254.5\end{array}$

(f)

To determine

To find: The standard deviation for the provided data set.

Answer to Problem 1PP

The standard deviation is 15.950

Explanation of Solution

Standard deviation for the provided data set is computed as:

  $\begin{array}{c}\text{Standard deviation}=\sqrt{\text{Variance}}\\ =\sqrt{254.5}\\ =15.950\end{array}$

Thus, the standard deviation is 15.950.

(g)

To determine

To find: The coefficient of variation.

Answer to Problem 1PP

The coefficient of variation is 12.176%

Explanation of Solution

The coefficient of variation can be computed as:

  $\begin{array}{c}CV=\frac{s}{\overline{x}}\times 100\\ =\frac{15.950}{131}\times 100\\ =12.176\end{array}$

The coefficient of variation is 12.176%.