Interpreting histograms - Teacher Slides.pptx

EDEXCEL GCSE MATHS · HIGHER

Interpreting histograms

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Lesson 5 of 6

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EDEXCEL GCSE MATHS · HIGHER

Warm-up

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Lesson 5 of 6

Answer each one, then check.

1

What is frequency density?

2

Work out 20 × 1.5.

3

What is the midpoint of the class 20 < x ≤ 40?

4

How do you estimate a mean from grouped data?

5

What is the median position for 124 values?

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EDEXCEL GCSE MATHS · HIGHER

Warm-up - Answers

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Lesson 5 of 6

1

What is frequency density?

Frequency divided by class width

2

Work out 20 × 1.5.

30

3

What is the midpoint of the class 20 < x ≤ 40?

30

4

How do you estimate a mean from grouped data?

Add up midpoint times frequency, divide by total frequency

5

What is the median position for 124 values?

The 62nd value

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Learning Objectives

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Lesson 5 of 6

1

Find frequencies from a histogram using area.

2

Estimate the number in part of a class.

3

Estimate the median from a histogram.

4

Estimate the mean from a histogram.

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EDEXCEL GCSE MATHS · HIGHER

Further statistics

Lesson 5 of 6

READING A HISTOGRAM

Frequency = frequency density × class width. That is the area of the bar.

To estimate a frequency for part of a class, use the width of just that part.

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Area Shows Frequency

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Area of the bar = frequency.

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Frequency from a Bar

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A histogram bar for the class 10 < t ≤ 30 has height 1.5. Find the frequency.

1

Class width

30 − 10 = 20

2

Multiply

20 × 1.5 = 30

ANSWER

The frequency is 30.

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Part of a Class

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In the class 20 < x ≤ 40 the frequency density is 2.2. Estimate the number of values between 25 and 40.

1

Width of the part

40 − 25 = 15

2

Multiply

15 × 2.2 = 33

ANSWER

About 33 values.

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Estimating the Median

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Lesson 5 of 6

Frequencies of 16, 30, 44, 24 and 10 are in classes 0−10, 10−20, 20−40, 40−70, 70−90 (total 124). The frequency density of 20−40 is 2.2. Estimate the median.

1

Position

124 ÷ 2 = 62

2

Running total

16 + 30 = 46, so the median is in 20−40

3

Values needed in this class

62 − 46 = 16

4

Width needed

16 ÷ 2.2 = 7.27

5

Median

20 + 7.27 = 27.3

ANSWER

The median is about 27.3.

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Estimating the Mean

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Lesson 5 of 6

Use the same data to estimate the mean.

1

Midpoints

5, 15, 30, 55, 80

2

Multiply

80 + 450 + 1320 + 1320 + 800 = 3970

3

Divide by 124

3970 ÷ 124 = 32.0

ANSWER

The mean is about 32.0.

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Reading Tips

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Lesson 5 of 6

Keep the method tidy.

Add a frequency column

Work out each bar's frequency first.

Running totals

Use them to find the median class.

Median

Interpolate inside the median class.

Estimates

Values from grouped data are only estimates.

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Key Terms

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Lesson 5 of 6

Frequency density

Height of a histogram bar.

Estimate

An approximate answer from grouped data.

Midpoint

The middle of a class.

Median class

The class that contains the median.

Interpolate

Find a value part of the way through a class.

Area

Width times height.

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Further statistics

Lesson 5 of 6

YOUR TASK

Read the Bars

12 minutes

A histogram has bars: 0−10 height 1.6, 10−20 height 3, 20−40 height 2.2, 40−70 height 0.8, 70−90 height 0.5. (a) Find each frequency. (b) Find the total. (c) Estimate the number aged 30 to 40.

1

Width times height.

2

Add them up.

WHAT A GOOD ANSWER SHOWS

(a) 16, 30, 44, 24, 10. (b) 124. (c) 10 × 2.2 = 22.

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Can I...?

Further statistics

Lesson 5 of 6

Find frequency from area.

Find the total frequency.

Estimate part of a class.

Find the median class.

Interpolate the median.

Work out midpoints.

Estimate the mean.

Explain why answers are estimates.

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Summary & Exam Focus

Frequency = frequency density × class width.

Median: find the class, then interpolate.

Mean: Σ(midpoint × frequency)/(total frequency).

Grouped answers are estimates.

EXAM FOCUS

The histogram shows the ages of visitors to a museum. Work out an estimate for the number of visitors aged 25 to 40. (3 marks)

Use the class width of only the part you need.

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Exam Practice: Interpreting histograms

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Lesson 5 of 6

Answer all questions. Show your working. · 30 minutes

Question 1 · 4 marks · Use the histogram

The histogram gives information about the ages of visitors to a museum. (a) Work out the number of visitors aged 10 to 20. (b) Work out an…

Question 2 · 2 marks · Work out

Use the same histogram to work out the total number of visitors.

Question 3 · 3 marks · Estimate

Use the same histogram to find an estimate for the median age.

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Exam Practice: Interpreting histograms (cont.)

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Lesson 5 of 6

Question 4 · 3 marks · Estimate

Use the same histogram to find an estimate for the mean age of the visitors.

Question 5 · 2 marks · Work out

A histogram bar for a class of width 20 has height 1.4. Work out the frequency of the class.

Question 6 · 2 marks · Explain

Explain why the answer to part (b) of the first question is only an estimate.

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Question 1 · 4 marks · Use the histogram

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Lesson 5 of 6

The histogram gives information about the ages of visitors to a museum. (a) Work out the number of visitors aged 10 to 20. (b) Work out an estimate for the number of visitors aged 25 to 40. (4 marks)

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Question 1 · mark scheme

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Lesson 5 of 6

4 marks available. Award a mark for each point made.

10 × 3

M1

30

A1

15 × 2.2

M1

33

A1

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Question 2 · 2 marks · Work out

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Lesson 5 of 6

“

Use the same histogram to work out the total number of visitors.

HOW TO ANSWER IT

Command word: Work out. Worth 2 marks, so plan before writing.

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Question 2 · mark scheme

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Lesson 5 of 6

2 marks available. Award a mark for each point made.

All five frequencies

M1

124

A1

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Question 3 · 3 marks · Estimate

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Lesson 5 of 6

“

Use the same histogram to find an estimate for the median age.

HOW TO ANSWER IT

Command word: Estimate. Worth 3 marks, so plan before writing.

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Question 3 · mark scheme

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Lesson 5 of 6

3 marks available. Award a mark for each point made.

Median position 62

B1

Interpolates in the class 20 to 40

M1

27.3 (accept 27 to 27.5)

A1

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Question 4 · 3 marks · Estimate

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Lesson 5 of 6

“

Use the same histogram to find an estimate for the mean age of the visitors.

HOW TO ANSWER IT

Command word: Estimate. Worth 3 marks, so plan before writing.

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EDEXCEL GCSE MATHS · HIGHER

Question 4 · mark scheme

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Lesson 5 of 6

3 marks available. Award a mark for each point made.

Midpoints times frequencies

M1

3970

A1

32.0

A1

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Question 5 · 2 marks · Work out

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Lesson 5 of 6

“

A histogram bar for a class of width 20 has height 1.4. Work out the frequency of the class.

HOW TO ANSWER IT

Command word: Work out. Worth 2 marks, so plan before writing.

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EDEXCEL GCSE MATHS · HIGHER

Question 5 · mark scheme

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Lesson 5 of 6

2 marks available. Award a mark for each point made.

Uses 20 × 1.4

M1

28

A1

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EDEXCEL GCSE MATHS · HIGHER

Question 6 · 2 marks · Explain

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Lesson 5 of 6

“

Explain why the answer to part (b) of the first question is only an estimate.

HOW TO ANSWER IT

Command word: Explain. Worth 2 marks, so plan before writing.

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Question 6 · mark scheme

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Lesson 5 of 6

2 marks available. Award a mark for each point made.

Data grouped

M1

Assumes even spread

C1

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