Question

ariana was looking at rent costs for 5 apartments. each rent was a different amount between $1,000 and $1,400 per month, except for one apartment whose rent was $4,800 per month. ariana looked at the mean and median of the rents. then, she decided to remove the $4,800 rent from the set and recalculate the mean and median. how will removing this rent affect the mean and median? choose 1 answer: a both the mean and median will increase, but the median will increase by more than the mean. b both the mean and median will increase, but the mean will increase by more than the median. c both the mean and median will decrease, but the median will decrease by more than the mean. d both the mean and median will decrease, but the mean will decrease by more than the median.

Explanation:

Step1: Understand mean and median concepts

Mean is sum of values divided by number of values. Median is middle - value when data is ordered.

Step2: Analyze the outlier effect on mean

The value $4800$ is an outlier (much larger than other values). The mean is affected by outliers. When we remove the outlier, the sum of values decreases by a large amount and the number of values decreases by 1. So the mean will decrease.

Step3: Analyze the outlier effect on median

We have 5 data - points originally. After removing one data - point, we have 4 data - points. Let the original ordered data be $a,b,c,d,4800$. The median of 5 data - points is $c$. After removing $4800$, the median of 4 data - points is the average of the two middle values. Since the outlier was the largest value, the new median will be smaller than the original median, but the decrease in median is less than the decrease in mean because the median is less affected by outliers.

Answer:

D. Both the mean and median will decrease, but the mean will decrease by more than the median.