Statistical Measures: Mean, Median, and Mode

Grade 6 · Math · Study Guide

Understand how to find and interpret the three main measures of center in a data set.

When we collect data, we often want one number that describes the 'center' of the data set. The three main measures of center are the mean, median, and mode.

The mean (average) is found by adding all the values together and dividing by the number of values. For example, the mean of 4, 7, 9, and 12 is (4 + 7 + 9 + 12) ÷ 4 = 32 ÷ 4 = 8.

The median is the middle value when the data is arranged in order from least to greatest. If there is an even number of values, the median is the average of the two middle values. For the data set 3, 6, 8, 10, the median is (6 + 8) ÷ 2 = 7.

The mode is the value that appears most often. A data set can have one mode, more than one mode, or no mode if all values appear the same number of times. For example, in 2, 4, 4, 7, 9, the mode is 4.

Each measure tells us something different. The mean uses all values but can be pulled by extreme numbers called outliers. The median is resistant to outliers. The mode tells us the most common value and is especially useful for non-numerical data. Choosing the right measure depends on the situation.

Key terms

Mean
The average; found by adding all values and dividing by the number of values
Median
The middle value of an ordered data set; or the average of the two middle values if there is an even count
Mode
The value that appears most frequently in a data set
Outlier
A data value that is much higher or lower than the other values; it can affect the mean significantly
Data Set
A collection of numbers or values gathered for analysis
Range
The difference between the greatest and least values in a data set

Flashcards

Mean formula
Sum of all values ÷ number of values
Median of an odd count
Order the values; the middle number is the median
Median of an even count
Order the values; average the two middle numbers
Mode
The most frequently occurring value(s) in a data set
Find mean of 5, 10, 15
(5 + 10 + 15) ÷ 3 = 30 ÷ 3 = 10
What is an outlier?
A value much larger or smaller than the rest; it pulls the mean toward it
Range formula
Greatest value − Least value
Which measure is most affected by outliers?
The mean; the median is resistant to outliers

Questions

  1. Find the mean of: 8, 10, 6, 12, 4.

    1. 6
    2. 8
    3. 10
    4. 7
    Show answer

    Answer: 8

    (8 + 10 + 6 + 12 + 4) ÷ 5 = 40 ÷ 5 = 8

  2. Find the median of: 3, 5, 7, 9, 11. The median is ___.

    Show answer

    Answer: 7

    Ordered: 3, 5, 7, 9, 11 — the middle value is 7

  3. A data set can have more than one mode.

    Show answer

    Answer: True

    A data set can have two modes (bimodal) or more if multiple values tie for most frequent

  4. Find the mode of: 2, 5, 3, 2, 7, 5, 2.

    1. 5
    2. 2
    3. 7
    4. 3
    Show answer

    Answer: 2

    2 appears 3 times, which is more than any other value

  5. The median of 4, 8, 10, 14 (even number of values) is ___.

    Show answer

    Answer: 9

    Order: 4, 8, 10, 14; two middle values are 8 and 10; (8 + 10) ÷ 2 = 9

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