Topic: Number

LO: Revision - Histograms.

PREPARE FOR LEARNING

AGREE LEARNING OBJECTIVES

Starter

Imagine you wanted to draw aBar Chart to show the followinginformation;

Height (cm) Frequency

100 < x ≤ 120 20

120 < x ≤ 140 25

140 < x ≤ 150 30

150 < x ≤ 160 25

160 < x ≤ 200 20

HISTOGRAMS

Starter

Height (cm) Frequency

100 < x ≤ 120

20

120 < x ≤ 140

25

140 < x ≤ 150

30

150 < x ≤ 160

25

160 < x ≤ 200

20

Height (cm)

Fre

quen

cy

0

5

20

15

10

100

25

120 180160140 200

REVIEW

Starter• Problems

1) The data is continuous so there should be no gaps

2) 150 – 160 has the same height as 120 – 140, even though it represents a smaller range

A Histogram will correct both of these problems!

Height (cm)

Fre

quen

cy

0

5

20

15

10

100

25

120 180160140 200

PRESENT NEW INFO

Histograms

20

25

30

25

20

Frequency

0.5160 < x ≤

200

2.5150 < x ≤

160

3140 < x ≤

150

1.25120 < x ≤

140

1100 < x ≤

120

Frequency Density

Height (cm) To take into account the size of the group, we calculate ‘Frequency Density’Frequency Density

FrequencyClasswidth

=

Frequency Density

2020

=

1=

3010

3=

2520

1.25=

2040

0.5=

2510

2.5=

CONSTRUCT MEANING

HistogramsHeight (cm) Frequency Frequency

Density

100 < x ≤ 120 20 1

120 < x ≤ 140 25 1.25

140 < x ≤ 150 30 3

150 < x ≤ 160 25 2.5

160 < x ≤ 200 20 0.5

100 140130120 150 160 180170110 200190

1

2

3

0

Fre

quen

cy D

ensi

ty

Height (cm)

CONSTRUCT MEANING

Histograms

With a Histogram, area represents Frequency, not the height

100 140130120 150 160 180170110 200190

1

2

3

0

Frequency

D

ensi

ty

Height (cm)

eg) The first group is a rectangle measuring 20 by 120 x 1 = 20 so there were 20 people in the group

eg) The fifth group is a rectangle measuring 40 by 0.540 x 0.5 = 20 so there were 20 people in the group

CONSTRUCT MEANING

Histograms

To take into account the size of the group, we calculate ‘Frequency Density’Frequency Density

FrequencyClasswidth

=

Frequency Density =

1040

0.25=

22070 < x ≤ 80

73565 < x ≤ 70

42060 < x ≤ 65

1.81850 < x ≤ 60

1.51540 < x ≤ 50

0.25100 < x ≤ 40

Frequency Density

FrequencySpeed (mph)

1810

1.8=

355

7=

205

4=

1510

1.5=

2010

2=

CONSTRUCT MEANING

HistogramsSpeed (mph) Frequency Frequency

Density

0 < x ≤ 40 10 0.25

40 < x ≤ 50 15 1.5

50 < x ≤ 60 18 1.8

60 < x ≤ 65 20 4

65 < x ≤ 70 35 7

70 < x ≤ 80 20 2

0 8040302010 6050 70

10

2

8

6

4

0

Fre

quen

cy D

ensi

ty

Speed (mph)

CONSTRUCT MEANING

Histograms

0 8040302010 6050 70

10

2

8

6

4

0

Frequency

Densi

ty

Speed (mph)

Group 1 is a 40 by 0.25 rectangle

40 x 0.25 = 10

So 10 people in the group

Remember that Area represents Frequency!Group 5 is a 5 by 7 rectangle

5 x 7 = 35

So 35 people in the group

CONSTRUCT MEANING

Your Turn…

(4)

33g

103g

Frequency Density

0.5

2.2

5.3

0.5

DEMONSTRATE UNDERSTANDING

Your Turn…

DEMONSTRATE UNDERSTANDING

EXTENSION: MORE HISTOGRAM QUESTIONS

Plenary

1

Frequency

Densi

ty

6

5

4

3

2

Egg Weight (g)

REVIEW

Summary• We have learnt how to plot Histograms of

sets of data

• We have seen how they are different to Bar Charts

• We have learnt what is meant by ‘Frequency Density’

• We have shown that on a Histogram, area represents Frequency, not height!

REVIEW