Mean, Median, Mode and Range

Understanding Mean, Median, Mode and Range

  • These are basic statistical measurements used to analyse a set of data.
  • They provide a simple and summary measure of your data and can be easily calculated.
  • It’s crucial to understand their differences and how to calculate each.

Mean

  • The mean is the typical average you are accustomed to.
  • Add all numbers in your data set and divide by the total count of numbers.
  • It considers every number in the dataset and is most affected by outliers (very high or very low numbers that are not typical).

Median

  • The median is the middle point of a data set.
  • When the numbers are listed in order from smallest to largest, the median is the number in the middle.
  • In a set with an even number of values, the median is the mean of the middle two numbers.
  • It isn’t as affected by outliers and can provide a more accurate picture of the data set’s centre when the data set contains extreme values.

Mode

  • The mode is the value that appears most frequently in a data set.
  • A set may have one mode, more than one mode, or no mode at all.
  • Modes aren’t necessarily in the middle of the data, and there can be more than one if several numbers appear with the same highest frequency.

Range

  • The range is the difference between the highest and lowest numbers in a data set.
  • This measure tells us how spread out the numbers in a data set are.
  • Like the mean, it is sensitive to extreme values and does not provide information about how the data is distributed between the high and low values.

Calculating and Interpreting Mean, Median, Mode and Range

  • These calculations are simple to perform and can provide useful insights about a data set.
  • The choice between mean, median, and mode depends on the type of data and the question you are trying to answer.

Example

  • Let’s take the set of numbers: 2, 3, 5, 5, 5, 7, 9
  • The mean makes it clear the average is (2+3+5+5+5+7+9)/7 = 5.14 (rounded)
  • The median number (in the middle) is 5.
  • The mode is also 5 (it appears most frequently).
  • The range is 7 (highest number 9 minus lowest number 2 gives us range).
  • It’s easy to see how each measure provides a slightly different view of this data set and its distribution.