Question

for the following set of numbers 13, 16, 12, 11, 8, 14, 12, and 18, which of the following is true?

• median>mean>mode
• mean>median>mode
• mean>mode>median
• media>mode>mean

Explanation:

Step1: Find the mode

The mode is the number that appears most frequently. In the set {13, 16, 12, 11, 8, 14, 12, 18}, 12 appears twice and others appear once. So mode = 12.

Step2: Find the median

First, sort the numbers: 8, 11, 12, 12, 13, 14, 16, 18. There are 8 numbers (even count), so median is the average of the 4th and 5th terms.
Median = $\frac{12 + 13}{2}$ = $\frac{25}{2}$ = 12.5

Step3: Find the mean

Mean = $\frac{Sum\ of\ all\ numbers}{Number\ of\ numbers}$
Sum = 8 + 11 + 12 + 12 + 13 + 14 + 16 + 18 = 104
Number of numbers = 8
Mean = $\frac{104}{8}$ = 13

Step4: Compare mode, median, mean

Mode = 12, Median = 12.5, Mean = 13
So mean (13) > median (12.5) > mode (12)

Answer:

mean>median>mode (the option with this text)