Mean, Median, Mode, Range
[Pages:35]FAC U LT Y O F E D U C AT I O N
Department of Curriculum and Pedagogy
Mathematics Mean, Median, Mode, Range
Science and Mathematics Education Research Group
Supported by UBC Teaching and Learning Enhancement Fund 2012-2013
Test Scores
Best Practices
When solving mean, median, mode and range questions, it is often very helpful to rewrite the data from smallest to largest.
13, 13, 13, 15, 16, 16, 16
Both the median and mode become
3
3
scores Median scores
easy to pick out after arranging the data into groups.
20, 20, 20, 40, 40, 70, 80 The range can be found by
subtracting the first data point from
3
2 1 1 the last one:
Mode = 20
Range = 80 ? 20 = 60
Best Practices II
It is often not necessary to calculate the exact mean (average) of a data set to solve a lot of these questions.
In many cases all you need to do is decide which data set has the larger or smaller mean by estimating:
64, 67, 76, 68, 74 Which data set has the larger mean?
76, 70, 80, 86, 79
Noticing patterns in a data set can sometimes make
calculating the mean easier.
Notice that 75 is 5 less than 80,
75, 75, 80, 80, 85, 85: Mean = 80 and 85 is 5 greater than 80
Test Scores I
Jeremy scored the following on his last seven math tests (out of 100):
70, 80, 70, 90, 80, 100, 70 What is the mean of Jeremy's test scores?
A. 280 B. 90 C. 80 D. 70 E. 30
Solution
Answer: C Justification: The mean is the average of the scores.
Note: Scores have been arranged from smallest to largest below.
M ean 70 70 70 80 80 90 100 7
560 7
80
Test Scores II
Jeremy scored the following on his last seven math tests (out of 100):
70, 80, 70, 90, 80, 100, 70 What is the median of Jeremy's test scores?
A. 100 B. 90 C. 80 D. 75 E. 70
Solution
Answer: C
Justification: The median is the score in the middle when arranged from least to greatest (or greatest to least).
70, 70, 70, 80, 80, 90, 100
3 scores
3 scores
Median
If there are 2 scores in the middle (due to an even number of scores), the median is the mean of those 2 scores.
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