Chapter 12.3, Problem 26PPE

To determine

To find: How does dividing each value in the data set by same nonzero amount affect the mean, median, mode, and range.

Answer to Problem 26PPE

When each value in a data set is divided by same amount the mean, median, mode, and range all are also divided by same amount.

Explanation of Solution

Given information:

Each value in a data set is divided by same nonzero amount.

Calculation:

Let us suppose there is a data set $4,6,6,8,16$ .

  $\begin{array}{l}\text{Here, mean}=\frac{4+6+6+8+16}{5}=8\\ \text{Median}=6\\ \text{Mode}=6\\ \text{Range}=16-4=12\end{array}$

Now let us divide each value in data set by same amount $2$ .

New data set would be $2,3,3,4,8$ .

  $\begin{array}{l}\text{Here, mean}=\frac{2+3+3+4+8}{5}=4\\ \text{Median}=3\\ \text{Mode}=3\\ \text{Range}=8-2=6\end{array}$

Therefore, when each value in a data set is divided by same amount the mean, median, mode, and range all are also divided by same amount.