Average: (sum of items) / (total number of items) --> ex. {3, 10, 5} average = (3 + 10 + 5) ÷ 3 = 18 ÷ 3 = 6 --> average = 6
Median: middle number or average of middle 2 numbers --> (ex. {4, 7, 10, 13, 14} median = 10; {4, 6, 8, 9} median = (6 + 8) / 2 = 7)
Mode: the most frequently occurring number or numbers --> ex. {-1, -2, 3, 7, 3, 14 and 21} mode = 3

SAMPLE PRACTICE QUESTIONS FOR AVERAGES, MEDIANS, AND MODES

1. Ben’s average for his first 2 tests is 86. There are 3 tests to determine his final grade.
    If he wants a 90 average, what is the least score he can earn on the third exam?

     Solution
     A) a = his first test score; b = his second test score; 86 = average of two tests
          So (a + b) / 2 = 86
          (a + b) = 172 ; the total points for the 1st and 2nd test = 172

     B) x = third test score; 3 = total tests; 90 = final average
          So (172 + x ) / 3 = 90 --> 172 + x = 270 --> x = 98

2. The median of 7 test scores is 86. The mode is 89. The average is 87, and the highest
     score is 99. If all the scores are integers, what is the least possible test score?

     Solution
     A) x = lowest possible score
               x, ___, ___, ___, ___, ___, ___

     B) median = 86
               x, ___, ___, 86, ___, ___, ___

     C) highest score = 99
               x, ___, ___, 86, ___, ___, 99

     D) mode = 89 (There must be at least two)
               x, ___, ___, 86, 89, 89, 99

     E) In order for x to be as small as possible, the two remaining test scores must be as high as possible: x, 84, 85, 86, 89, 89, 99.

     F) Now that all the numbers have been found, an average equation can be set up.
               (x + 84 + 85 + 86 + 89 + 89 + 99) ÷ 7 = 87 --> x = 77

SAT Math: Average, Median, and Mode Practice

Lesson Includes:

—Math Terms for Averages, Medians, and Modes

—Sample Practice Questions

—Practice Questions

Math

SAT Reading

SAT Writing

SAT Vocabulary

AVERAGE, MEDIAN, AND MODE REVIEW QUIZ

 

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