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19.1 Interpreting and drawing frequency diagrams

19.1 Interpreting and drawing frequency diagrams

In stage 8 you drew frequency diagrams for discrete and The frequency diagrams you
continuous data. drew in stage 8 were bar charts.

You can also draw a frequency polygon for continuous data.

!is is a useful way to show patterns, or trends, in the data.
To draw a frequency polygon, you plot the frequency against the midpoint of the class interval.

Worked example 19.1

Jeff grew 40 seedlings.
He grew 20 in a greenhouse and 20 outdoors. The heights of the Height, h (cm) Frequency
20 seedlings grown in the greenhouse are shown in the table. 0 ≤ h < 10 2
a Draw a frequency polygon for the data in the table.
The frequency polygon shows the heights of the 20 seedlings grown outdoors. 10 ≤ h < 20 4
Heights of seedlings grown outdoors 20 ≤ h < 30 8
10
30 ≤ h < 40 6
8
Frequency 6 4

2
0
0 10 20 30 40
Height (cm)

b Compare the two frequency polygons (this one and the one you have drawn).
What can you say about the heights of the two sets of seedlings?

a Before you can draw the frequency polygon you
Height, h (cm) Frequency Midpoint need to work out the midpoints. Add an extra
0 ≤ h < 10 2 5 column to the table for these values. The midpoint
10 ≤ h < 20 4 15 of the class 0 ≤ h < 10 is 5. The midpoint of the
20 ≤ h < 30 8 25 class 10 ≤ h < 20 is 15, and so on.
30 ≤ h < 40 6 35

Heights of seedlings Now draw the frequency polygon. Extend the
grown in greenhouse horizontal scale to 40 cm. Extend to vertical
10 scale to at least 8. Plot the midpoints against
8 the frequency, then join the points in order with
straight lines. Remember to give the chart a title
Frequency 6 4 and label the axes.

2
0
0 10 20 30 40
Height (cm)

b The seedlings that were grown in the greenhouse Compare the two polygons and make a
grew higher than the seedlings that were grown general comment, describing the similarities
outdoors. 14 of the seedlings grown in the or differences. Include a numerical comparison
greenhouse were over 20 cm tall, whereas only 6 of to show that you clearly understand what the
the seedlings grown outdoors were over 20 cm tall. charts show.

178 19 Interpreting and discussing results