If the integer 135 is removed from the data set containing the integers 3, 15, 42, 180, 135, 43, 3, 42, 12, 210 and the mean, the median, and the range are recalculated, which of the following will change?
A) Mean
B) Median
C) Range
D) All of them
Maps to Category 64 of my book.
Answer posted on 10/10/2021: Correct answer choice is A.
Order the numbers least to greatest: 3, 3, 12, 15, 42, 42, 43,135, 180, 210.
Median:
The median of data set is the average of the 5th and the 6th number. Since both the numbers are 42, the median is 42.
After removing 135, the numbers are 3, 3, 12, 15, 42, 42, 43,180, 210. The median is the 5th number = 42. Hence, the median does not change. This eliminates answer choices B and D.
Range:
Since the lowest and the highest numbers of the data set remain the same after removing 135, the range does not change. This eliminates answer choice C.