Averages from Tables | CIE IGCSE Maths: Core Revision Notes 2023

Averages from Tables & Charts

How do we find averages if there are lots of values?

In reality there will be far more data to work with than just a few numbers
In these cases the data is usually organised in such a way to make it easier to follow and understand
- For example in a table or chart
We can still find the mean, median and mode but have to ensure we understand what the table or chart is telling us

How do I find averages from a table or chart?

Finding the median and mode from tables/charts is fairly straightforward once you understand what the table/chart is telling you
Tables allow data to be summarised neatly
- and quite importantly, they put the data into order

Finding the mean from data presented in tables

The mean can be found as you long as understand what a table is telling you
- Tables tell us the data value
  - e.g. the number of pets per household
- and the frequency of that data value
  - e.g. the number of households with that number of pets

   STEP 1
   Add a column to the table and work out "data value" × "frequency"
   (This is effectively doing the 'adding up' part of finding the mean in stages)

   STEP 2
   Find the total of the extra column to give the overall total of the data values

   STEP 3
   Find the mean by dividing this total by the total of the frequency column
   i.e. divide the total of the data values by the number of data values

Finding the median from data presented in tables

The median is the middle value when the data is in order
The position of the median can be found by using $\frac{n + 1}{2}$ , where $n$ is the number of data values
Use the table to deduce where the ${(\frac{n + 1}{2})}^{th}$ value lies
- e.g. if the median is the 7^th value and the frequency of the first two rows are 4 and 7
  - the median will be one of the 7 values the second row of that table

Finding the mode (or modal value)

The mode (or modal value) is simple to identify
- Look for the highest frequency
  - and thus find the corresponding data value
- Make sure you do not confuse the data value with the frequency!
  - The frequency (in a table) tells us the row the mode is in

Finding the range

Look at the data column (not the frequency column)
- Subtract the lowest value from the highest value

Worked example

The bar chart shows data about the shoe sizes of pupils in class 11A.

Bar Chart Shoe Size, IGCSE & GCSE Maths revision notes

Find the mean shoe size for the class,

Although the data is given in a bar chart, this is essentially the same as a table.
Rewrite it as a table but add an extra column to help find the total of all the shoe sizes.

Shoe size (x )	Frequency (f )	xf
6	1	6 × 1 = 6
6.5	1	6.5 × 1 = 6.5
7	3	7 × 3 = 21
7.5	2	7.5 × 2 = 15
8	4	8 × 4 = 32
9	6	9 × 6 = 54
10	11	10 × 11 = 110
11	2	11 × 2 = 22
12	1	12 × 1 = 12
Total	31	278.5

Mean $= \frac{278.5}{31} = 8.983 870 . . .$

Mean = 8.98 (3 s.f.)

Note that the mean does not have to be an actual shoe size.

Find the median shoe size,

The bar chart/table has the data in order already so find the position of the median.

$\frac{n + 1}{2} = \frac{31 + 1}{2} = \frac{32}{2} = 16$

The median is the 16^th value.
There are 1 + 1 + 3 + 2 + 4 = 11 values in the first five rows of the table.
There are 11 + 6 = 17 values in the first six rows of the table.
Therefore the 16^th value must be in the sixth row.

Median shoe size is 9

Suggest a reason the shop owner may wish to know the modal shoe size of their customers.

A shop owner would want to know the modal shoe size of their customers as this size will be more likely to sell than other sizes so the shop owner should order more shoes in the modal size to stock the shop with

Averages from Tables (CIE IGCSE Maths: Core)

Revision Note

Averages from Tables & Charts

How do we find averages if there are lots of values?

How do I find averages from a table or chart?

Worked example

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Author: Paul