Chapter 11.6, Problem 28PPSE

Solution

Toidentify:Theeffect on mean, median mode, range, and box and whisker plot if adding 10 to every value in a data set, if multiply each value by 10.

Adding 10 to every value of the data set also add 10 to the mean and if multiply 10 to every value, then mean is increased by 10 times. Same will happen for mode and median.

If every value is added by 10 then there will be no change in range but rage will increase by 10 times if every value is multiplied by 10.

Given information:

It is given that add 10 to each value and multiply each value by 10.

Explanation:

Consider the given information.

Let the data set is 2, 2, 3, 4, 4, 5, 5, 5.

So, the mean is:

  $\begin{array}{c}Mean=\frac{2+2+3+4+4+5+5+5}{8}\\ =3.75\end{array}$

Now add 10 to each value.

  $\begin{array}{c}Mean=\frac{12+12+13+14+14+15+15+15}{8}\\ =13.75\\ =\overline{x}+10\end{array}$

Now multiply 10 to each value.

  $\begin{array}{c}Mean=\frac{20+20+30+40+40+50+50+50}{8}\\ =37.5\\ =\overline{x}\cdot 10\end{array}$

Hence adding 10 to every value of the data set also add 10 to the mean and if multiply 10 to every value, then mean is increased by 10 times.

Let the data is 2, 2, 3, 4, 4, 5, 5, 5 adding 10 will gives us 12, 12, 13, 14, 14, 15, 15, 15.

Multiplying 10 will gives us 20, 20, 30, 40, 40, 50, 50, 50.

Draw box and whisker plot

  

Now observe that median of the original data set is 4, if add ten then median is 14 and if multiplied by 10 then median is 40. Thus, median is also multiplied by 10.

Mode of the original data set was 5, if add ten then mode is 15 and if multiplied by 10 then mode is 50. Thus, mode is also multiplied by 10.

The range of the original data set was $5-2=3$ .

If add ten then range is $15-12=3$

If multiplied by 10 then rage is $50-20=30$