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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