Question

from unit 1, lesson 10 the data show the number of free throws attempted by a team in its first 10 games. 2 11 11 11 12 12 13 14 14 15 the median is 12 attempts and the mean is 11.5 attempts. after reviewing the data, it is determined that 2 should not be included, since that was an exhibition game rather than a regular game during the season. a. what happens to the median if the “2” is removed from the data set? b. what happens to the mean if the “2” is removed from the data set?

Explanation:

Step1: Analyze the original data set for median

The original data set has 10 values. Arranged in ascending - order: 2, 11, 11, 11, 12, 12, 13, 14, 14, 15. The median of a set with 10 values is the average of the 5th and 6th ordered values. $\text{Median}=\frac{12 + 12}{2}=12$.

Step2: Analyze the new data set for median

After removing 2, the data set has 9 values: 11, 11, 11, 12, 12, 13, 14, 14, 15. The median of a set with 9 values is the 5th ordered value, which is 12. So the median remains 12.

Step3: Analyze the original data set for mean

The mean of the original data set $\bar{x}_1=\frac{2 + 11+11+11+12+12+13+14+14+15}{10}=11.5$.

Step4: Analyze the new data set for mean

The sum of the new data set (after removing 2) is $11+11+11+12+12+13+14+14+15 = 113$. The new mean $\bar{x}_2=\frac{113}{9}\approx12.56$. Since $12.56>11.5$, the mean increases.

Answer:

a. The median remains the same.
b. The mean increases.