Question

Ariana was looking at rent costs for 5 apartments. Each rent was a different amount between 1,000 and1,400 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 the4,800 rent from the set and recalculate the mean and median. How will removing this rent affect the mean and median?

1) The mean will decrease and the median will stay the same.
2) The mean will increase and the median will stay the same.
3) The mean will stay the same and the median will decrease.
4) The mean will stay the same and the median will increase.

Answer 1

Removing the $4,800 rent will cause the mean to decrease due to the elimination of an outlier, while the median will remain the same because the middle values are unaffected.

Step-by-step explanation:

When dealing with the mean and median, it is essential to understand their sensitivity to extreme values or outliers. The mean is the average value calculated by summing all the rents and dividing by the number of rents. The median is the middle value when the rents are ordered from the smallest to largest. If there are any outliers, such as an exceptionally high rent, they can skew the mean much more than the median.

In Ariana's case, if she removes the $4,800 rent, which is significantly higher than the other rents, the mean will decrease because the sum of the rents will decrease while the number of rents considered reduces by only one. Since the $4,800 rent is the highest value, it has a significant influence on the mean. However, the median, which is the middle value, will stay the same as it is determined by the middle rents, which are unaffected by the highest rent when it is removed, assuming there is an odd number of rents remaining.

Therefore, the correct response is that the mean will decrease and the median will stay the same after the $4,800 rent is removed from the dataset.