Chapter 10.1, Problem 1GP

To determine

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

Answer to Problem 1GP

The Mean is $158$ , Median is $157$ and there is no Mode.

Explanation of Solution

Given information: The table shows the winning speeds of the Indianapolis $500$ in recent year.

Calculation : The table shows the winning speeds of the Indianapolis $500$ in recent year.

Given data is $157,152,144,150,162,170,168$ .

Mean of data is:

  $\begin{array}{l}\mathrm{Mean}=\frac{sumofdata}{\mathrm{number}\mathrm{of}\mathrm{data}}\\ \mathrm{Mean}=\frac{157+152+144+150+162+170+168}{7}=\frac{1103}{7}=157.57\\ \mathrm{Round}\mathrm{off}(157.57)=158\end{array}$

Median of the data:

Data in ascending order $144,150,152,157,162,168,170$ .

  $\begin{array}{l}\mathrm{n}=7\\ \mathrm{Median}=\frac{n+1}{2}=\frac{7+1}{2}=\frac{8}{2}th=4th\\ 4th\mathrm{term}\mathrm{is}157\\ \end{array}$

So median is $157$ .

Mode:

In this case, none of the items are more frequent. So there is no mode.

Thus, the Mean is $158$ , Median is $157$ and there is no Mode.