Question 1 The list of numbers 41, 35, 30, X, Y, 15 has a median of 25 and the mode is 15. What is the mean?

-- Answer -- 26

The median is 25 => (30 + X) / 2 = 25. X = 20

The mode is 15 => Y = 15

The mean = (41 + 35 + 30 + 20 + 15 + 15)/6 = 26

Question 2 The mean of 5 integers is 52. The median of these 5 integers is 82. Three of the integers are 0, 12, and 82. Which of the following could be one of the other integers….52, 66, 84, 86, 105?

-- Answer -- 84

The sum of the other 2 integers is

5 * 52 – 0 – 12 – 82 = 166

52: The integers would be 0, 12, 52, 82, 114….82 is not the median

66: The integers would be 0, 12, 66, 82, 100…82 is not the median

84: The integers would be 0, 12, 82, 82, 84…82 is the median

86: The integers would be 0, 12, 80, 82, 86…82 is not the median

105: The integers would be 0, 12, 61, 82, 86, 105…82 is not the median

Question 3 What is the difference between the mean and median based on the histogram below.

-- Answer -- 0.9

Data Set = {1, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 5, 5, 6, 7, 8}

Median = (3 + 4) / 2 = 3.5

Mean = (1 * 1 + 2 * 3 + 3 * 4 + 4 * 3 + 5 * 2 + 6 * 1 + 7 * 1 + 8 * 1) / 14 = 4.4

Difference = mean – median = 4.4 – 3.5 = 0.9