the fuel economies in miles per gallon (mpg) for nine vehicles are listed below. 16, 18, 20, 24, 24, 24, 24…

Explanation:

Step1: Calculate the original mean

The formula for the mean $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}$. Here, $n = 9$, and $\sum_{i=1}^{9}x_{i}=16 + 18+20 + 24+24+24+24+31+32=213$. So the original mean $\bar{x}_1=\frac{213}{9}\approx23.67$.

Step2: Calculate the new mean

After adding a value of 40, $n = 10$, and $\sum_{i = 1}^{10}x_{i}=213 + 40=253$. The new mean $\bar{x}_2=\frac{253}{10}=25.3$. The mean increases.

Step3: Calculate the original median

For $n = 9$ (odd - numbered data set), the median is the $\left(\frac{n + 1}{2}\right)$-th value. $\frac{9+1}{2}=5$-th value. The ordered data set is $16,18,20,24,24,24,24,31,32$, and the median $M_1 = 24$.

Step4: Calculate the new median

For $n = 10$ (even - numbered data set), the median is the average of the $\frac{n}{2}$-th and $\left(\frac{n}{2}+1\right)$-th values. $\frac{10}{2}=5$ and $\frac{10}{2}+1 = 6$. The ordered data set is $16,18,20,24,24,24,24,31,32,40$. The median $M_2=\frac{24 + 24}{2}=24$. The median does not change.

Answer:

The mean will increase and the median will not change.