Drawing histograms.pptx

EDEXCEL GCSE MATHS · HIGHER

Drawing histograms

Further statistics

Lesson 4 of 6

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EDEXCEL GCSE MATHS · HIGHER

Warm-up

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Lesson 4 of 6

Answer each one, then check.

1

What is the width of the class 10 < t ≤ 30?

2

Work out 30 ÷ 20.

3

What is a frequency table?

4

How does a bar chart differ from a histogram?

5

Write 12 ÷ 10 as a decimal.

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EDEXCEL GCSE MATHS · HIGHER

Warm-up - Answers

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Lesson 4 of 6

1

What is the width of the class 10 < t ≤ 30?

20

2

Work out 30 ÷ 20.

1.5

3

What is a frequency table?

A table of how often values occur

4

How does a bar chart differ from a histogram?

A histogram's bar area shows frequency; classes are continuous

5

Write 12 ÷ 10 as a decimal.

1.2

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EDEXCEL GCSE MATHS · HIGHER

Learning Objectives

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Lesson 4 of 6

1

Explain why a histogram uses frequency density.

2

Work out the frequency density for each class.

3

Draw a histogram with unequal class widths.

4

Label the axes correctly.

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EDEXCEL GCSE MATHS · HIGHER

Further statistics

Lesson 4 of 6

HISTOGRAM

In a histogram the area of each bar shows the frequency. The height is the frequency density.

frequency density = frequency/(class width). The bars touch and there are no gaps.

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A Histogram

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Lesson 4 of 6

Wider bars are shorter for the same frequency.

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Working Out Frequency Density

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Lesson 4 of 6

Times taken (t minutes) by 94 customers.

Time

Frequency

Class width

Frequency density

0 < t ≤ 10

12

10

1.2

10 < t ≤ 30

30

20

1.5

30 < t ≤ 40

26

10

2.6

40 < t ≤ 60

18

20

0.9

60 < t ≤ 100

8

40

0.2

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EDEXCEL GCSE MATHS · HIGHER

Drawing a Histogram

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Lesson 4 of 6

Follow the steps.

1

Work out the class widths

Upper boundary minus lower boundary

2

Work out the frequency density

Frequency divided by class width

3

Draw the axes

Data on the horizontal axis, frequency density on the vertical axis

4

Draw the bars

Bars touch; the height is the frequency density

5

Label

Add a scale and a label for each axis

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EDEXCEL GCSE MATHS · HIGHER

Frequency Density

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Lesson 4 of 6

A class 20 < x ≤ 50 has frequency 60. Work out the frequency density.

1

Class width

50 − 20 = 30

2

Divide

60/30 = 2

ANSWER

The frequency density is 2, so the bar has height 2.

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Completing a Histogram

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Lesson 4 of 6

Age (a years): 0 < a ≤ 10: 8, 10 < a ≤ 20: 20, 20 < a ≤ 40: 36, 40 < a ≤ 60: 30. The first three bars are drawn. Work out the height of the last bar.

1

Class width

60 − 40 = 20

2

Frequency density

30/20 = 1.5

ANSWER

Draw a bar from 40 to 60 with height 1.5.

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Common Mistakes

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Lesson 4 of 6

Watch for these.

Frequency as the height

Use frequency density.

Gaps between bars

The bars must touch.

Widths

Use the actual class width, not the number of classes.

Labels

The vertical axis is "Frequency density", not "Frequency".

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Key Terms

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Lesson 4 of 6

Histogram

A chart where bar area shows frequency.

Frequency density

Frequency divided by class width.

Class width

The upper boundary minus the lower boundary.

Continuous data

Data measured, not counted.

Unequal class widths

Classes of different sizes.

Area

Height multiplied by width.

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Further statistics

Lesson 4 of 6

YOUR TASK

Find the Density

10 minutes

Work out the frequency density for each class. (a) 0 < w ≤ 5, frequency 15 (b) 5 < w ≤ 15, frequency 40 (c) 15 < w ≤ 35, frequency 30 (d) 35 < w ≤ 60, frequency 10.

1

Class width first.

2

Then divide.

WHAT A GOOD ANSWER SHOWS

(a) 3 (b) 4 (c) 1.5 (d) 0.4

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Can I...?

Further statistics

Lesson 4 of 6

Find the class widths.

Work out frequency density.

Draw and label axes.

Draw bars that touch.

Use unequal class widths.

Complete a partly drawn histogram.

Explain why frequency density is used.

Avoid common mistakes.

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EDEXCEL GCSE MATHS · HIGHER

Summary & Exam Focus

Frequency density = frequency/(class width).

Area of bar = frequency.

Bars touch; classes may have different widths.

The vertical axis is frequency density.

EXAM FOCUS

A table shows the ages of 94 people in classes with different widths. Work out the frequency density for each class and draw the histogram. (4 marks)

Add a frequency density column to the table first.

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