Chapter 13.2, Problem 12PPS

(a)

To determine

To Find:Themeasure of central tendency would the Rams want to use to show they have a greater number of points scored per game than the stallions.

Answer to Problem 12PPS

Mode

Explanation of Solution

Given:The back to back stem-and-leaf plot at the right shows the points scored by the high school football teams in their games this season.

  

Which measure of central tendency would the Rams want to use to show they have a greater number of points scored per game than the stallions? Explain.

For Rams

Finding Mean

  $\begin{array}{l}\text{Mean=}\frac{\text{sum of observation}}{\text{total number of observation}}\\ Mean=\frac{7+8+9+14+15+18+19+20+24+24}{10}\\ Mean=\frac{159}{10}=15.8\end{array}$

Mean= $15.8$

Finding Median:

Arranging the number in ascending order.

The data is even thus

Take the middle number.

  $\begin{array}{l}7,8,9,14,\underset{\_}{15,18,}19,20,24,24\\ Median=\frac{15+18}{2}=16.5\end{array}$

Hence

Median= $16.5$

Finding Mode:

  $24$ is most repeating.

Mode= $24$

For Stallions:

Finding Mean

  $\begin{array}{l}\text{Mean=}\frac{\text{sum of observation}}{\text{total number of observation}}\\ Mean=\frac{10+10+15+19+20+21+22+25+28+31}{10}\\ Mean=\frac{201}{10}=20.1\end{array}$

Mean= $20.1$

Finding Median:

Arranging the number in ascending order.

The data is even thus

Take the middle number.

  $\begin{array}{l}10,10,15,19,\underset{\_}{20,21},22,25,28,31\\ Median=\frac{20+21}{2}=20.5\end{array}$

Hence

Median= $20.5$

Finding Mode:

  $10$ is most repeating.

Mode= $10$

From comparing Rams and stallions

It is concluded that

Mode is the measure of central tendency would they want to use to show they have a greater number of points scored per game than the stallions

(b)

To determine

To Find: Themeasure of central tendency would the stallions want to use to show they have a greater number of points scored per game than the Rams.

Answer to Problem 12PPS

Mean and Median

Explanation of Solution

Given: The back to back stem-and-leaf plot at the right shows the points scored by the high school football teams in their games this season.

  

Which measure of central tendency would the stallions want to use to show they have a greater number of points scored per game than the Rams? Explain.

For Rams

Finding Mean

  $\begin{array}{l}\text{Mean=}\frac{\text{sum of observation}}{\text{total number of observation}}\\ Mean=\frac{7+8+9+14+15+18+19+20+24+24}{10}\\ Mean=\frac{159}{10}=15.8\end{array}$

Mean= $15.8$

Finding Median:

Arranging the number in ascending order.

The data is even thus

Take the middle number.

  $\begin{array}{l}7,8,9,14,\underset{\_}{15,18,}19,20,24,24\\ Median=\frac{15+18}{2}=16.5\end{array}$

Hence

Median= $16.5$

Finding Mode:

  $24$ is most repeating.

Mode= $24$

For Stallions:

Finding Mean

  $\begin{array}{l}\text{Mean=}\frac{\text{sum of observation}}{\text{total number of observation}}\\ Mean=\frac{10+10+15+19+20+21+22+25+28+31}{10}\\ Mean=\frac{201}{10}=20.1\end{array}$

Mean= $20.1$

Finding Median:

Arranging the number in ascending order.

The data is even thus

Take the middle number.

  $\begin{array}{l}10,10,15,19,\underset{\_}{20,21},22,25,28,31\\ Median=\frac{20+21}{2}=20.5\end{array}$

Hence

Median= $20.5$

Finding Mode:

  $10$ is most repeating.

Mode= $10$

From comparing Rams and stallions

It is concluded that

Mean and Median is the measure of central tendency would Stallion want to use to show they have a greater number of points scored per game than the Rams