Question

the fuel economies in miles per gallon (mpg) for nine vehicles are listed below.
16, 18, 20, 24, 24, 24, 24, 31, 32
if one more vehicle is added to the list with a rate of 40 mpg, how will this affect the mean and median?
the mean and median will both increase.
the mean will increase and the median will decrease.
the mean will increase and the median will not change.
the mean will decrease and the median will not change.

Explanation:

Step1: Calculate original mean

Original sum: $16+18+20+24+24+24+24+31+32 = 213$. Mean: $\frac{213}{9} \approx 23.67$.

Step2: Find original median

9 values, median is 5th value: 24.

Step3: Calculate new mean

New sum: $213+40=253$. Mean: $\frac{253}{10}=25.3$ (increased).

Step4: Find new median

10 values, median is average of 5th and 6th values: $\frac{24+24}{2}=24$ (unchanged).

Answer:

C. The mean will increase and the median will not change.