This section looks at a number of the key statistical graphs required for GCSE Mathematics.

It will also show how you can find averages from a given graph.

Being able to read and then relate the information which a graph shows is an important skill in real-life

Cumulative Frequency Graph

If we are given a table containing continuous data, we can find a running total of the frequency. This is called Cumulative Frequency.

 Height (m) Frequency Cumulative Frequency In context 7 7 7 people less than 1.4m 8 15 15 people less than 1.6m 22 37 37 people less than 1.8m 3 40 40 people less than 2.0m

We can therefore plot a graph:

·       The x-axis (horizontal) will be Height(m)

·       The y-axis will (vertical) will be Cumulative Frequency

·       We plot the numbers in red

·       The graph starts at 1.2m, because this was the lowest value   We can now use this graph to estimate a number of key values

In this case n=40 (the total number of people

Median: On a cumulative frequency graph we find value We can read this off the graph to get 1.64m

Lower Quartile: On a cumulative frequency graph we find value We can read this off the graph to get 1.48m

Upper Quartile: On a cumulative frequency graph we find value We can read this off the graph to get 1.73m

From this we can deduce the IQR = UQ - LQ = 1.73m-1.48m=0.25m

Histogram – the A/A* graph!

Suppose you are given a table of continuous data (see below).

Given a class eg. the class width is In the table below, you can see how the class widths change.

In this case, we will need to construct a histogram to represent the data.

In a histogram, the AREA of the bars equals the FREQUENCY

To achieve this, we need to calculate a value called the FREQUENCY DENSITY Height (m) Frequency class-width Frequency density 5 0.2 25 12 0.3 40 15 0.3 50 2 0.1 20

We now draw a graph with:

·       Height(m) on the x-axis

·       Frequency density on the y-axis The next section considers how to read graphs to find an average

Finding the mean and median from a frequency graph

A frequency graph to show the frequency of scores in a test This graph can be turned into a frequency table

 Mark Midpoint Frequency 5 8 15 12 25 11 35 3 TOTAL 34    