Chapter 13.1, Problem 8PPS

(a)

To determine

To Find: If she score her lowest score, which measure of central tendency would increase more, the mean and the median? Explain.

Answer to Problem 8PPS

The measure of central tendency has increased more in Median than Mean

Explanation of Solution

Given:Sasha scored the following point total in $7$ games this basketball season: $12,18,20,8,15,18,14$

Case I

Finding Mean:

  $\begin{array}{l}\text{Mean=}\frac{\text{sum of observation}}{\text{total number of observation}}\\ Mean=\frac{12+18+20+8+15+18+14}{7}\\ Mean=\frac{105}{7}=15\end{array}$

Mean = $15$

Finding Median:

Arranging the number in ascending order.

The data is odd thus

Take the middle number.

  $8,12,14,15,18,18,20$

Hence

Median= $15$

Case second:

If we goes to the lowest amount we get the mean and median as

Finding Mean:

  $\begin{array}{l}\text{Mean=}\frac{\text{sum of observation}}{\text{total number of observation}}\\ Mean=\frac{12+18+20+15+18+14}{6}\\ Mean=\frac{97}{6}=16\end{array}$

Mean= $16$

Finding Median:

After removing the lowest score, the number of observations is even

Thus,

Median

  $\begin{array}{l}12,14,\underset{\_}{15,18},18,20\\ median=\frac{15+18}{2}=17\end{array}$

Median= $17$

From comparing case I with case II

It is concluded that

The measure of central tendency has increased more in Median than Mean.

(b)

To determine

To Find:In her next basketball game, Sasha scores $13$ points .Which measure of central tendency would decrease more the mean or median? Explain.

Answer to Problem 8PPS

The measure of central tendency has decreased equally in Median and Mean.

Explanation of Solution

Given: Sasha scored the following point total in $7$ games this basketball season: $12,18,20,8,15,18,14$

Case I

Finding Mean:

  $\begin{array}{l}\text{Mean=}\frac{\text{sum of observation}}{\text{total number of observation}}\\ Mean=\frac{12+18+20+8+15+18+14}{7}\\ Mean=\frac{105}{7}=15\end{array}$

Mean = $15$

Finding Median:

Arranging the number in ascending order.

The data is odd thus

Take the middle number.

  $8,12,14,15,18,18,20$

Hence

Median= $15$

Case second:

Sasha scores $13$ points so the data will increase to $8$ we get the mean and median as

Finding Mean:

  $\begin{array}{l}\text{Mean=}\frac{\text{sum of observation}}{\text{total number of observation}}\\ Mean=\frac{12+18+20+15+18+14+8+13}{8}\\ Mean=\frac{118}{8}=14.5\end{array}$

Mean= $14.5$

Finding Median:

Median

  $\begin{array}{l}8,12,13,\underset{\_}{14,15},18,18,20\\ median=\frac{15+14}{2}=14.5\end{array}$

Median= $14.5$

From comparing the mean and median of case I with case II

  $\begin{array}{l}Mean=14.5-15=-0.5\\ Median=14.5-15=-0.5\end{array}$

It is concluded that

The measure of central tendency has decreased equally in Median and Mean.