Central Tendency

Words of “Wiz-dom”There are three measures of central tendency that the test writer expects you to know: mean (average), median, and mode. There is not a pattern that compares them. Each can be larger or smaller than the other two. For example, the mean could be the smallest, the middle or the largest of the three. The same is true of the other two.

Mean: You are most familiar with this indicator of central tendency. It is the mathematical average. The standard formula is:

A more useful form of this standard equation is to multiply the mean times the number of scores to calculate the sum of the scores.  Quite often on the test you will be given the number of scores and the mean and you’ll need to calculate the sum in order to answer the question.  Keep this in mind anytime you see a mean question.

A group of students took a math test and their scores were: 78, 82, 84, 87, 89, 90, 92, 96, 96, and 96. What was their average (mean) score?

Answer Mean

Words of “Wiz-dom”-For questions about means, the key is the sum of the scores. The test writer will commonly tell you the mean and the number of the scores and you have to calculate the sum of the scores to answer the question.

Median: The score that is in the middle when the scores are ranked in ascending or descending order. If you have an even number of scores, then the median is half way between (the mean of) the two scores that are in the middle.

What is the median of the scores for the math class?

Answer Median

Mode: The score that occurs most frequently in a group of scores. There can be more than one most common score. However, if all scores occur an equal number of times, there is no mode.

What is the mode of the above list of scores?

Answer Mode

Sample Questions

3.  The School of Wiz-dom basketball team had an average (mean) score of 71 points for its first 5 games of the season. What was the total number of points they had scored?

(A) 355
(B) 365
(C) 375
(D) 385
(E) 425

Answer to Question #3

15. Five truck drivers averaged using 62 gallons of fuel driving between Wiz-land and Bonterra. Four of the truckers used an average of 60 gallons. How many gallons of fuel did the fifth driver use?

(A) 60
(B) 61
(C) 62
(D) 66
(E) 70

Answer to Question #15

19.  An alchemist averaged using 88 ingredients in her first 5 potions and 96 ingredients in the next 3. What was her average number of ingredients?

(A) 88
(B) 90
(C) 91
(D) 92
(E) 94

Answer to Question #19

12.  On a biology quiz, 7 students got an 80, 10 got a 90, and 3 got a 100. What was the average score for these students?

(A) 80
(B) 88
(C) 90
(D) 92
(E) 100

Answer to Question #12

15. Four of the five knights who guard The Wiz’s personal tower average 5 feet 10 inches tall. How tall is the fifth knight if all five knights average 6 feet tall?

(A) 6 feet
(B) 6 feet and 2 inches
(C) 6 feet and 4 inches
(D) 6 feet and 6 inches
(E) 6 feet and 8 inches

Answer to Question #15

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