Averages (SQA National 5 Applications of Mathematics): Revision Note

Mode, median & mean

What is the mode?

• The mode of a data set is the value that appears the most often

  • The mode of 1, 2, 2, 5, 6 is 2

• There can be more than one mode

  • The modes of 1, 2, 2, 5, 5, 6 are 2 and 5

• There might not be a mode

  • The data set 1, 2, 3, 4 does not have a mode

  • Do not say the mode is zero

What is the median?

• The median of a data set is the middle value when you put values in size order

  • The median of 4, 2, 3 can be found by

    • ordering the numbers: 2, 3, 4

    • and choosing the middle value, 3

• If you have an even number of values, find the midpoint of the middle two values 

  • The median of 1, 2, 3, 4 is 2.5

    • 2.5 is the midpoint of 2 and 3

  • The midpoint is the sum of the two middle values divided by 2

What is the mean?

• The mean of a data set is the sum of the values divided by the number of values

  • The mean of 1, 2, 6 is (1 + 2 + 6) ÷ 3 = 3

• The mean of a data set is sometimes represented by

  • Then the mean can be written as a formula

    • is the sum of all the data values

    • is the number of data values

  • This formula is not given to you in the exam

• The mean can be a fraction or a decimal

  • It may need rounding

  • You do not need to force it to be a whole number

    • You can have a mean of 7.5 people, for example!

What are the differences between the mode, median and mean?

• The mode, median and mean are different ways to measure an average

• In certain situations it is better to use one average over another

• For example:

  • Use the median instead of the mean if there are extreme values (outliers)

    • The mean of 1, 1, 2, 3, 5, 5, 5, 25 is affected by the 25 but the median is not

  • You should only use the mode if the data is non-numerical

    • Such as types of pets or favourite colours