# Average

Words of “Wiz-dom”—The ACT test writer tests three measures of central tendency: mean, median, and mode.  They are all indicators of “average” or “typical” indicators of a group of measurements.

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.

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.

Mean: For questions about “mathematical averages”or more commonly the “mean,” 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.

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?

### Sample Questions:

 1 Four of the five knights who guard The Wiz’s personal tower average 5 feet and ten 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

 2 Five truck drivers averaged using 62 gallons of fuel driving between Wizland 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

 3 An alchemist averaged using 88 ingredients on her first 5 potions and 96 ingredients on the next 3. What was her average number of ingredients?A. 88 B. 90 C. 91 D. 92 E. 94