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Exam code:C300

Mean, median & mode

What is the mode?

  • The mode 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

  • The mode can also be called the modal value

What is the median?

  • The median 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 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 can be 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!

How do I know when to use the mode, median or 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:

    • If the data has extreme values (outliers) like 1, 1, 4, 50
      The mode is 1
      The median is 2.5
      The mean is 14

      • Don’t use the mean (it’s badly affected by extreme values)

    • If the data has more than one mode 

      • Don’t use the mode as it is not clear

    • If the data is non-numerical, like dog, cat, cat, fish

      • You can only use the mode

Worked Example

15 students were timed to see how long it took them to solve a mathematical problem. Their times, in seconds, are given below.

12

10

15

14

17

11

12

13

9

21

14

20

19

16

23

(a) Find the mean time, giving your answer to 3 significant figures.

 Add up all the numbers (you can add the rows if it helps) 

12 + 10 + 15 + 14 + 17 = 68
11 + 12 + 13 + 9 + 21 = 66
14 + 20 + 19 + 16 + 23 = 92

Total = 68 + 66 + 92 = 226 

Divide the total by the number of values (there are 15 values)

table row cell 226 over 15 end cell equals cell 15.066 space 666 space... end cell end table

Write the mean to 3 significant figures
Remember to include the units

The mean time is 15.1 seconds (to 3 s.f.)

(b) Find the median time.

Write the times in order and find the middle value

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