Chapter B.2, Problem 12E

(a)

To determine

To find: The mean, median and mode of the revised data.

Answer to Problem 12E

The explanation is given below.

Explanation of Solution

Given:

Add 6 to each number in exercise 8.

The new data is:

  $\left\{23,43,38,45,39,40,38\right\}$

Arrange the above data in ascending order.

  $\left\{23,38,38,39,40,43,45\right\}$

The mean, median and mode of above data is calculated as:

  $\begin{array}{c}\text{Mean}=\frac{23+38+38+39+40+43+45}{7}\\ =38\\ \text{Mode}=38\\ \text{Median}=\left(\left(\frac{N+1}{2}\right)\text{th term}\right)\end{array}$

Further simplified as:

  $\begin{array}{c}\text{Median}=\left(4\text{th term}\right)\\ =39\end{array}$

Arrange the data of exercise 8 in ascending order.

  $\left\{17,32,32,33,34,37,39\right\}$

The mean, median and mode of exercise 7 is calculated as:

  $\begin{array}{c}\text{Mean}=\frac{17+32+32+33+34+37+39}{7}\\ =32\\ \text{Mode}=32\\ \text{Median}=\left(\left(\frac{N+1}{2}\right)\text{th term}\right)\end{array}$

Further simplified as:

  $\begin{array}{c}\text{Median}=\left(4\text{th term}\right)\\ =33\end{array}$

The mode, median and mode of revised data also increased by the value 6 in compare to data given in exercise 8.

Therefore, the comparison is given above.

(b)

To determine

To find: The change in measure of central tendency of data of exercise 8 if a constant $k$ is added to each number.

Answer to Problem 12E

The explanation is given below.

Explanation of Solution

Case 1: If constant $k$ is greater than zero.

Then after the constant $k$ added to each number of the data, the mean, median and mode will increase by the value $k$ .

Case 1: If constant $k$ is less than zero.

Then after the constant $k$ added to each number of the data, the mean, median and mode will decrease by the value $k$ .

Therefore, the explanation is given above.