Question

at track practice, alexia ran 5 attempts of the 100 - meter dash. all of her times were different values between 11 and 13 seconds, except for an attempt when she tripped and finished in 24 seconds. alexias coach said they would remove the 24s result from the set of these practice times. how will removing this time affect the mean and median? choose 1 answer: a both the mean and median will decrease, but the mean will decrease by more than the median. b both the mean and median will decrease, but the median will decrease by more than the mean. c both the mean and median will increase, but the mean will increase by more than the median. d both the mean and median will increase, but the median will increase by more than the mean.

Explanation:

Step1: Understand mean and median concepts

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

Step2: Analyze the effect on the mean

The 24 - second value is an outlier (much larger than other values). The mean is affected by outliers. When we remove the 24 - second value, the sum of the remaining data decreases by 24, and the number of data - points decreases by 1. Since the outlier was increasing the mean, removing it will decrease the mean.

Step3: Analyze the effect on the median

We have 5 data - points originally. When ordered, the median is the 3rd value. Removing the outlier (24), we still have 4 data - points. The new median is the average of the 2nd and 3rd ordered values. Since the outlier was the largest value, the new median will be less than the old median, but the change in the median is less significant than the change in the mean because the median only depends on the middle value(s) and not on the sum of all values.

Answer:

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