How to calculate averages from a list of data:
Robert is preparing for his Mathematics GCSE exams. Each
paper is marked out of 100. He attempts 10 tests and gets the following scores:
63, 86, 64, 67, 71, 42, 79, 64, 80, 64.
We can use these values to calculate the mean, median and
mode to find out more information about his scores.
The mean
The mean uses all the
values in the data. To calculate the mean:
- Add all the numbers up
- Divide by how many values
there are:
63 + 86 + 64 + 67 + 71 + 42 + 79 + 64 + 80 + 6410 = 68010 = 68
Mean = 68
The median
The median is
the middle value in the sorted set of data. To calculate the median:
- List the values in order
from smallest to largest
- Cross values off from each
end to identify the middle value
If there are two numbers in the
middle you must calculate the mean of these two values. This means we add them
up and divide by 2.
Order: 42, 63, 64, 64, 64,
67, 71, 79, 80, 86
Middle: 64, 67
64 + 672 = 1312 = 65.5
Median = 65.5
The mode
The mode is the
most common value that appears in the data.
The mode is the only average where there can be
more than one. If there are two modes we say it is bimodal; if there are
more than two modes it is multimodal. If all the values appear the same
number of times, we can say there is no mode.
It is often useful to use
the ordered set of numbers; 42, 63, 64, 64, 64, 67, 71, 79, 80,
86.
Mode = 64
The value 64 appears three
times. All the rest appear only once.
