Measures of central tendency and dispersion

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  • Measures of central tendency and dispersion
    • Central tendencies - a descriptive statistic that provides information about a 'typical' value for a data set.
      • Mean
        • It  is the most sensitive measure of central tendency, so it takes account of the exact distance between all the values of all the data.
        • However, this sensitivity means it can be distorted by extreme values and end up being a misrepresentation of the data as a whole.
      • Median
        • It is not affected by extreme values, so they won't distort it.
        • It doesn't reflect the exact values so isn't as sensitive.
      • Mode
        • It is the only method that can be used when the data is in categories, for example nominal data.
        • There can be several modes, which makes it hard to describe data.
    • Dispersion - a  descriptive statistic that provides information about how spread out a set of data is.
      • Range - difference between top and bottom values. It is customary to add 1 (15-3+1) because 15 could represent a value as big as 15.5 and 3 could represent a value as low as 2.5.
        • It is easy to calculate.
        • It fails to take account of the distribution of the numbers. E.g. it doesn't show whether most numbers are closely grouped around the mean or spread out evenly.
      • Standard deviation is a measure of the spread of data around the mean.It shows the amount of variation in a data set.
        • However it may hide some characteristics of the data set, such as extreme values.
        • It is a precise measure of dispersion because it takes all the exact values into account.

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