5 from unit 1, lesson 10 the data show the number of free throws attempted by a team in its first 10 games…

5 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?
Answer
Explanation:
Step1: Organize data without 2
The original data set is 2, 11, 11, 11, 12, 12, 13, 14, 14, 15. After removing 2, the new data - set is 11, 11, 11, 12, 12, 13, 14, 14, 15.
Step2: Calculate new median
Since there are 9 data points, the median is the 5th - ordered value. The 5th value in the ordered new data - set is 12. The original median was 12. So the median remains the same.
Step3: Calculate original sum
The original sum of the data set (S_1=2 + 11+11+11+12+12+13+14+14+15=115).
Step4: Calculate new sum
The new sum of the data set (S_2=11 + 11+11+12+12+13+14+14+15 = 113).
Step5: Calculate new mean
The new number of data points (n = 9). The new mean (\bar{x}=\frac{S_2}{n}=\frac{113}{9}\approx12.56). The original mean was 11.5. So the mean increases.
Answer:
a. The median remains the same. b. The mean increases.