Chapter 7.1, Problem 25E

To determine

To find:

The mean, median, and mode of given data.

Answer to Problem 25E

  $\text{Mode}=5$ , $M_d=7$ , $\overline{X}=8$

Explanation of Solution

Given:

The data value increases by $4$

Concept used:

The median is the middle number in a sorted ascending or descending list of numbers and more descriptive of that data set than the average.

Calculation:

A real number k is added to each value in a numerical data set the measures of center of the new data set is found by adding k to the original measures of center.

The original measures of center are

The mean

  $\overline{X}=4$

The median is the middle number

  $M_d=3$

The mode (the most frequent number)

  $\text{Mode}=1$

By adding the value of $4$ of the new measures of center

The mean

  $\begin{array}{l}\overline{X}=4+4\\ \overline{X}=8\end{array}$

The median is the middle number

  $\begin{array}{l}{M}_d=3+4\\ M_d=7\end{array}$

The mode (the most frequent number)

  $\begin{array}{l}\text{Mode}=1+4\\ \text{Mode}=5\end{array}$