Chapter 0, Problem 30PR

a.

To determine

To calculate:Mean

Answer to Problem 30PR

The mean value of the data set is 10.5294

Explanation of Solution

Given information:

  $\text{10,15,9,8,11,10,9,8,13,9,12,10,13,11,9,12,10}$

Number of terms= 17

Used formula:

  $Mean=\frac{sumofterms}{Numberofterms}$

Calculation:

The mean of a data set is the sum of the terms divided by the total number of terms. Using math notation, we have:

  $Mean=\frac{sumofterms}{Numberofterms}$

Sum of terms $=\text{10,15,9,8,11,10,9,8,13,9,12,10,13,11,9,12,10}=179$

Numbers of terms=17

  $\begin{array}{l}Mean=\frac{sumofterms}{Numberofterms}\\ =\frac{179}{17}\\ =10.5294\end{array}$

b.

To determine

To calculate: Median

Answer to Problem 30PR

The median value of the data set is 10

Explanation of Solution

Given information:

  $\text{10,15,9,8,11,10,9,8,13,9,12,10,13,11,9,12,10}$

Number of terms= 17

Calculation:

(ii) The median is the middle number in a sorted list of numbers. So, to find the median, we need to place the numbers in value order and find the middle number.

Ordering the data from least to greatest, we get:

  $8 ,8 ,9 ,9 ,9 ,9 ,10 ,10 ,10 ,10 ,11 ,11 ,12 ,12 ,13 ,13 ,15$

So, the median is 10.

c.

To determine

To calculate: Mode

Answer to Problem 30PR

The mode value of the data set is 9 and 10

Explanation of Solution

Given information:

  $\text{10,15,9,8,11,10,9,8,13,9,12,10,13,11,9,12,10}$

Number of terms= 17

Calculation:

(iii) The mode of a set of data is the value in the set that occurs most often.

Ordering the data from least to greatest, we get:

  $8 ,8 ,9 ,9 ,9 ,9 ,10 ,10 ,10 ,10 ,11 ,11 ,12 ,12 ,13 ,13 ,15$

Since both 9 and 10 occur 4 times, the modes are 9 and 10 (this data set is bimodal).

d.

To determine

To calculate: Range

Answer to Problem 30PR

The range value of the data set is 7

Explanation of Solution

Given information:

  $\text{10,15,9,8,11,10,9,8,13,9,12,10,13,11,9,12,10}$

Number of terms= 17

Calculation:

(iv) The range is the difference between the highest and lowest values in the data set.

Ordering the data from least to greatest, we get:

  $8 ,8 ,9 ,9 ,9 ,9 ,10 ,10 ,10 ,10 ,11 ,11 ,12 ,12 ,13 ,13 ,15$

The lowest value is 8.

The highest value is 15.

The range $=15-8=7.$

e.

To determine

To calculate: Standard deviation

Answer to Problem 30PR

The standard deviation value of the data set is $\sigma$ :1.8823529411765

Explanation of Solution

Given information:

  $\text{10,15,9,8,11,10,9,8,13,9,12,10,13,11,9,12,10}$

Number of terms= 17

Used formula:

  $\sigma =\sqrt{\frac{1}{N}{\displaystyle \sum _{i=1}^n{(X_i-\mu )}^2}}$

Calculation:

  $\begin{array}{l}Count,N:17\\ Sum,\Sigma x:179\\ Mean,\mu :10.529411764706\\ Variance,{\sigma }^2: 3.5432525951557\end{array}$

  $\begin{array}{l}\sigma =\sqrt{\frac{1}{N}{\displaystyle \sum _{i=1}^n{(X_i-\mu )}^2}}\\ {\sigma }^2=\frac{{\displaystyle \sum (x_i}-\mu {)}^2}{N}\\ {\sigma }^2=\frac{{(10-10.529411764706)}^2+\mathrm{...}+{\left(10-10.529411764706\right)}^2}{17}\\ {\sigma }^2=\frac{\begin{array}{c}60.235294117647\end{array}}{17}\\ {\sigma }^2=3.5432525951557\\ \begin{array}{ll}\sigma =\hfill & \surd 3.5432525951557\hfill \end{array}\\ \sigma \begin{array}{rr}\hfill = & \hfill 1.8823529411765\end{array}\end{array}$

f.

To determine

To calculate: Outliers

Answer to Problem 30PR

No any outliers

Explanation of Solution

Given information:

  $\text{10,15,9,8,11,10,9,8,13,9,12,10,13,11,9,12,10}$

Number of terms= 17

Calculation:

There have no any outliers because no have any common number in the given question.