Measures of Central Tendency

Definition of Measures of Central Tendency

A measure of central tendency is a measure that tells us where the middle of a bunch of data lies.

The three most common measures of central tendency are the mean, the median, and the mode.

More About Measures of Central Tendency

  • Mean: Mean is the most common measure of central tendency. It is simply the sum of the numbers divided by the number of numbers in a set of data. This is also known as average.
  • Median: Median is the number present in the middle when the numbers in a set of data are arranged in ascending or descending order. If the number of numbers in a data set is even, then the median is the mean of the two middle numbers.
  • Mode: Mode is the value that occurs most frequently in a set of data.

Video Examples: Measures of Central Tendency


Examples of Measures of Central Tendency

    For the data 1, 2, 3, 4, 5, 5, 6, 7, 8 the measures of central tendency are
    Mean = Examples of   Measures of Central Tendency
    Median = 5
    Mode = 5

Solved Example on Measures of Central Tendency

Ques: Find the measures of central tendency for the data set 3, 7, 9, 4, 5, 4, 6, 7, and 9.

    Choices:
    A. Mean = 6, median = 6 and modes are 4, 7 and 9
    B. Mean = 6, median = 6 and mode is 4
    C. Mean = 6, median = 6 and modes are 4 and 9
    D. Mean = 6, median = 9 and modes are 4, 7 and 9
    Correct Answer: A

Solution:

    Step 1: Mean, median and mode of a data set are the measures of central tendency.
    Step 2: Mean of the data set = Examples of   Measures of Central Tendency [Formula.]
    Step 3: Examples of   Measures of Central Tendency [Substitute the values.]
    Step 4: Examples of   Measures of Central Tendency [Add the data values in the numerator and divide.]
    Step 5: The data set in the ascending order is 3, 4, 4, 5, 6, 7, 7, 9, and 9. So, Median of the set is 6. [Median is the middle data value of the ordered set.]
    Step 6: Mode is/are the data value(s) that appear most often in the data set. So, the modes of the data set are 4, 7 and 9.
    Step 7: So, the measures of central tendency of the given set of data are mean = 6, median = 6 and modes are 4, 7, and 9.