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Measures of Central Tendency and Variability

This topic covers measures of central tendency and variation. We learn to find appropriate measures of central tendency and variability. We also learn how to make box-and-whisker plots and interpret them.

Topic: Measures of Central Tendency

  • Measures of central tendency are numbers that describe the middle of a data set. The most common measures are mean, median, and mode

  • To find the mean, add the values in the data set. Then divide by the number of values in the set

  • Median is the middle value, or the mean of two middle values, in an ordered set of data

  • Mode is the value(s) that occur most frequently. A data set may have no mode, one mode, or several modes

  • Use mean when the data does not have any outliers (extreme values).
    Use median when the data does have outliers (extreme values) and there are no big gaps in the data.
    Use mode when the data has many identical numbers

Topic: Measures of Variation

  • Measures of variation are used to describe the distribution of the data. They indicate how “spread out’ the data is. Some of the measures are: range, quartiles, and interquartile range

  • Range is the difference between the least and the greatest values in the data set. Median = Middle value (in case of odd number of values) and mean of two middle values (in case of even number of values)

  • First/Lower quartile = Median of the lower half of the data. Third/Upper quartile = Median of the upper half of the data

  • The interquartile range is the range of the middle half of the data. It is the difference between the upper quartile and the lower quartile

  • Data that are more than 1.5 times the value of the interquartile range beyond the quartiles are called outliers

Topic: Box-and-Whisker Plots

  • A box-and-whisker plot shows the distribution of data. It separates data into four equal parts

  • The middle half of the data is represented by a ‘box’ with a vertical line at the median. The lower quartile and upper quartile are represented by ‘whiskers’ that extend to the smallest and largest values

  • A long whisker or box indicates that the data in that quartile or quartiles have a greater range. A shorter whisker or box indicates that the data in that quartile or quartiles have a lesser range

  • If there is an outlier in the data, the whisker is drawn till the end of the least/greatest value that is not an outlier
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