Question

1. the box - plot represents the distribution of the number of children in 30 different families. after further examination, the value of 12 is removed for having been recorded in error. the box - plot represents the distribution of the same data set, but with the maximum, 12, removed. the median is 2 children for both plots. a. explain why the median remains the same when 12 was removed from the data set. b. when 12 is removed from the data set, does the mean remain the same? explain your reasoning.

Explanation:

a. The median is the middle - value. With 30 data points, the median is the average of the 15th and 16th ordered values. Removing the maximum value (12) does not change the position of these middle - values. So the median remains the same.
b. The mean is the sum of all values divided by the number of values. The value 12 is the maximum. When it is removed, the sum of the data set decreases while the number of data points also decreases by 1. Since 12 is a large value, the sum will decrease more proportionally than the decrease in the number of data points. So the mean will decrease and not remain the same.

Answer:

a. The median is based on the middle - values and removing the maximum does not change the middle - values for 30 data points.
b. No, because the large value of 12 affects the sum more than the decrease in the number of data points when removed.