Mean, Median & Mode (Edexcel IGCSE Maths)

Spec point — 6.2B

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.

Answer:

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)

$\begin{gathered} \frac{226}{15} & = 15.066 666 ... \end{gathered}$

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

Final answer: The mean time is 15.1 seconds (3 s.f.)

(b) Find the median time.

Answer:

Write the times in order and find the middle value

$\cancel{9} \cancel{10} \cancel{11} \cancel{12} \cancel{12} \cancel{13} \cancel{14} \text circled{14} \cancel{15} \cancel{16} \cancel{17} \cancel{19} \cancel{20} \cancel{21} \cancel{23}$

Final answer: The median time is 14 seconds

(c) Explain why the median is a better measure of average time than the mode.

Answer:

Try to find the mode (the number that occurs the most)

There are two modes: 12 and 14

Explain why the median is better

Final answer: There is no clear mode (there are two modes, 12 and 14), so the median is better

(d) If a 16th student has a time of 95 seconds, explain why the median of all 16 students would be a better measure of average time than the mean.

Answer:

The16th value of 95 is extreme (very high) compared to the other values Means are affected by extreme values

Final answer: The mean will be affected by the extreme value of 95 whereas the median will not