Learning Objectives :Learning Objectives :

6.5 Understand the concept of6.5 Understand the concept of

cumulative frequencycumulative frequency

Learning Outcomes:Learning Outcomes:

Students will be able forStudents will be able for

i) Construct the cumulative frequency table for:a) ungrouped datab) grouped data

ii) Draw the ogive for:a) ungrouped datab) grouped data

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WorksheetsWorksheets• Worksheet 1

• Worksheet 2

• Worksheet 3

•Lesson Plan 1•Lesson Plan 2•Lesson Plan 3

Lesson Plan

6.5 (i) How to construct the cumulative 6.5 (i) How to construct the cumulative frequency table? frequency table?

Ungrouped data Ungrouped data Group data. Group data.

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21211st card

10102nd card

15153rd card

12124th card

17175th card

+ = ?

10+21 = 31

21211st card

10102nd card

+

31

+ = ?

+ 15 = 46

21211st card

10102nd card

15153rd card

2121 1010 1515 1212+ + =

46

+1st card 2nd card 3rd card 4th card

+ 12 = 58

?

+

+

+ = ?

78 + 17 = 95

21211st card

10102nd card

15153rd card

12124th card

17175th card

Ungrouped DataUngrouped Data

Score 0 1 2 3 4

Frequency 2 5 3 7 3

ScoreUpper

boundaryFrequency

Cumulative Frequency

0 0.5 2

1 1.5 5

2 2.5 3

3 3.5 7

4 4.5 3

Example 1

2

7

10

17

20

Example 2 :

Marks 20 25 30 35 40

Frequency 7 16 22 13 2

MarksUpper

BoundaryFrequency

Cumulative Frequency

20

25

30

35

40

Ungrouped DataUngrouped Data

Example 2 :

Marks 20 25 30 35 40

Frequency 7 16 22 13 2

MarksUpper

BoundaryFrequency

Cumulative Frequency

15 15.5 0

20 20.5 7

25 25.5 16

30 30.5 22

35 35.5 13

40 40.5 2

Ungrouped DataUngrouped Data

0

7

23

45

58

60

Marks 51- 60 61-70 71- 80 81- 90 91-100

Frequency 7 8 13 9 3

MarksUpper

BoundaryFrequency

Cumulative Frequency

41-50 50.5 0

51-60 60.5 7

61-70 70.5 8

71-80 80.5 13

81-90 90.5 9

91-100 100.5 3

Example 3 : Grouped DataGrouped Data

ExercisesExercisesWorksheet 1Worksheet 1

Fill in the tablesFill in the tables

Instructions: Constructs the cumulative frequency table base on the table below.

Age

(year)16 17 18 19 20

Frequency 27 23 25 16 19

Worksheet 1Worksheet 1

Instructions:Construct the cumulative frequency base onthe table below.

Volume of petrol (litre)

10-14 15-19 20-24 25-29 30-34

Frequency 7 10 6 3 4

Worksheet 2Worksheet 2

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6.5 (ii) Draw the ogive for6.5 (ii) Draw the ogive for (a) Ungrouped data (a) Ungrouped data

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Height (cm) 163 164 165 166 167 168

Frequency

Upper Boundary

165 167 164 165 164

168 165 163 164 165

ANSWER

Table 1: Data of the heights of the basketball players

Height (cm) 163 164 165 166 167 168

Frequency 1 3 4 0 1 1

Upper Boundary

163.5 164.5 165.5 166.5 167.5 168.5

165 167 164 165 164

168 165 163 164 165

Table 1: Data of the heights of the basketball players

Table 2 : Data of the marks of the students of the Form 4 Cerdik 

60 75 82 61 90 91 98 68 75 78

56 53 98 68 65 61 61 70 69 75

56 80 83 80 99 75 75 78 78 56

Marks 51-60 61-70 71-80 81-90 91-100

Frequency

         

Upper Boundary

         

ANSWER

Table 2 : Data of the marks of the students of the Form 4 Cerdik 

60 75 82 61 90 91 98 68 75 78

56 53 98 68 65 61 61 70 69 75

56 80 83 80 99 75 75 78 78 56

Marks 51-60 61-70 71-80 81-90 91-100

Frequency

 5 7   10  3 4 

Upper Boundary

 60.5

 70.5

 80.5

 90.5

 100.5

The above table shows the frequency of weight of the The above table shows the frequency of weight of the cakes sold in a shop on a particular day. Using the data cakes sold in a shop on a particular day. Using the data given , construct a table of cumulative frequency. Then, given , construct a table of cumulative frequency. Then, draw the ogive with a scale of 2 cm to 1 kg at x-axis and draw the ogive with a scale of 2 cm to 1 kg at x-axis and 2 cm to 5 unit at y-axis .2 cm to 5 unit at y-axis .

Weight of cake (kg)

1 2 3 4 5

Frequency 4 6 10 4 1

EXAMPLEEXAMPLE

WHAT IS AN OGIVE?WHAT IS AN OGIVE?

An ogive is a chart of cumulative frequency

Conditions of drawing the ogive

• Using the cumulative frequency • Add a class before the first interval class • Write as zero in the cumulative frequency

Weight of cakes (kg)

Upper boundary

Frequency Cumulative frequency

0

1 4

2 6

3 10

4 4

5 1

0.5

1.5

2.5

3.5

4.5

5.5

0 0

4

10

20

24

25

COMPLETE A TABLE BELOW

ADD A CLASS FOR ZERO FREQUENCY BEFORE THE FIRST CLASS

HOW TO DRAW AN OGIVEHOW TO DRAW AN OGIVE1. CONSTRUCT THE CUMULATIVE FREQUENCY TABLE

2. DRAW AN X-AXIS FOR THE UPPER BOUNDARIES AND A

Y-AXIS FOR THE CUMULATIVE FREQUENCY BASED ON THE

GIVEN SCALE

3. PLOT THE POINTS

4. JOIN ALL THE POINTS WITH A SMOOTH CURVE

5. LABEL THE GRAPH

Weight of cakes (kg)

Upper boundary

Frequency Cumulative frequency

0

1 4

2 6

3 10

4 4

5 1

0.5

1.5

2.5

3.5

4.5

5.5

0 0

4

10

20

24

25

THE CUMULATIVE FREQUENCY TABLE(Ungrouped data)

5. JOIN ALL THE POINTS SMOOTHLY

4. LABEL 4. LABEL THE GRAPHTHE GRAPH

1. PLOT 1. PLOT THE THE

POINTSPOINTS

3. CONSTRUCT THE CUMULATIVE FREQUENCY TABLE

2. DRAW THE 2. DRAW THE X AND Y AXESX AND Y AXES

HOW TO HOW TO DRAW DRAW

AN OGIVEAN OGIVE

1.5 2.5 3.5 4.5 5.5

5

10

15

20

25

0.5 Weight of the cakes (kg)

x

Cumulative Frequency

y OgiveOgive

Weight of cakes (kg)

Upper boundary

Frequency Cumulative frequency

0

1

2

3

4

5

0.5

1.5

2.5

3.5

4.5

5.5

0

4

6

10

4

1

0

4

10

20

24

25

THE CUMULATIVE FREQUENCY TABLE

ExercisesExercisesWorksheet 2Worksheet 2

Fill in the tablesFill in the tables

Draw the ogives respectivelyDraw the ogives respectively

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Learning Objectives :Learning Objectives :

6.5 Understand the concept of6.5 Understand the concept of

cumulative frequencycumulative frequency

6.1 (ii) Draw the ogive for6.1 (ii) Draw the ogive for (b) Grouped data (b) Grouped data

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Bar-ChartBar-Chart

0

10

20

30

40

50

60

70

80

90

100

1.5 2.5 3.5 4.5

HistogramHistogram

Distribution of story books borrowed by a group of students in February

4-6

7-9

10-12

13-15

16-18

0

2

4

6

8

10

12

1

The number of story books

Fre

quency

3.5 6.5 9.5 12.5 15.5 18.5

Frequency PoligonFrequency PoligonDistribution of story books borrowed by a

group of students in February

0

2

4

6

8

10

12

2 5 8 11 14 17 20

The number of story books

frequency

1.5 2.5 3.5 4.5 5.5

5

10

15

20

25

0.5 Weight of the cakes (kg)

x

Cumulative Frequency

y OgiveOgive

5. JOIN ALL THE POINTS SMOOTHLY

4. LABEL 4. LABEL THE GRAPHTHE GRAPH

3. PLOT 3. PLOT THE THE

POINTSPOINTS

1. CONSTRUCT THE CUMULATIVE FREQUENCY TABLE

2. DRAW THE 2. DRAW THE X AND Y AXESX AND Y AXES

HOW TO HOW TO DRAW DRAW

AN OGIVEAN OGIVE

Step 1 Step 1 Complete the cumulative frequency tableComplete the cumulative frequency table

Volume of Water

Upper Boundary

FrequencyCumulative frequency

0

1.2 - 1.4 6

1.5 - 1.7 9

1.8 - 2.0 16

2.1 - 2.3 5

2.4 - 2.6 3

2.7 - 2.9 1

1.45

1.75

2.05

2.35

2.65

2.95

1.15 0

6

15

31

36

39

40

Step 2 Step 2 Draw the scales respectivelyDraw the scales respectively

Volume of Water

Upper Boundary

FrequencyCumulative frequency

1.15 0 0

1.2 - 1.4 1.45 6 6

1.5 - 1.7 1.75 9 15

1.8 - 2.0 2.05 16 31

2.1 - 2.3 2.35 5 36

2.4 - 2.6 2.65 3 39

2.7 - 2.9 2.95 1 40

x-axis : upper boundaries

y-axis : Cumulative frequency

40

30

20

10

Volume of water

2.05 2.35 2.65 2.95

Cumulative frequency

1.15 1.45 1.75

Step 3 - plot the points Step 3 - plot the points

Volume of Water

Upper Boundary

FrequencyCumulative frequency

1.15 0 0

1.2 - 1.4 1.45 6 6

1.5 - 1.7 1.75 9 15

1.8 - 2.0 2.05 16 31

2.1 - 2.3 2.35 5 36

2.4 - 2.6 2.65 3 39

2.7 - 2.9 2.95 1 40

40

30

20

10

Volume of water

2.05 2.35 2.65 2.95

Cumulative frequency

1.15 1.45 1.75

Step 4 - join the points smoothly Step 4 - join the points smoothly

Volume of Water

Upper Boundary

FrequencyCumulative frequency

1.15 0 0

1.2 - 1.4 1.45 6 6

1.5 - 1.7 1.75 9 15

1.8 - 2.0 2.05 16 31

2.1 - 2.3 2.35 5 36

2.4 - 2.6 2.65 3 39

2.7 - 2.9 2.95 1 40

40

30

20

10

Volume of water

2.05 2.35 2.65 2.95

Cumulative frequency

1.15 1.45 1.75

1.5 2.5 3.5 4.5 5.5

5

10

15

20

25

0.5 Weight of the cakes (kg)

x

Cumulative Frequency

y OgiveOgive

ExercisesExercisesWorksheet 3Worksheet 3

Fill in the tablesFill in the tables

Draw the ogives respectivelyDraw the ogives respectively

Table 1 - Table 1 - worksheet 3worksheet 3

Volume of Water

Upper Boundary

FrequencyCumulative frequency

1.2 - 1.4 61.5 - 1.7 91.8 - 2.0 162.1 - 2.3 52.4 - 2.6 32.7 - 2.9 1

Table 2 - Table 2 - worksheet 3worksheet 3

Height (cm)Upper

BoundaryFrequency

Cumulative frequency

0110 - 119 10120 -129 16130 - 139 20140 - 149 34150 - 159 52160 - 169 32170 - 179 12180 - 189 4

Table 3 - Table 3 - worksheet 3worksheet 3

ScoreUpper

BoundaryFrequency

Cumulative frequency

04.1 - 5.0 25.1 - 6.0 46.1 - 7.0 77.1 - 8.0 208.1 - 9.0 289.1 - 10.0 1210.1 - 11.0 511.1 - 12.0 2

1.5 2.5 3.5 4.5 5.5

5

10

15

20

25

0.5 Weight of the cakes (kg)

x

Cumulative Frequency

y OgiveOgive

5. JOIN ALL THE POINTS SMOOTHLY

4. LABEL 4. LABEL THE GRAPHTHE GRAPH

1. PLOT 1. PLOT THE THE

POINTSPOINTS

3. CONSTRUCT THE CUMULATIVE FREQUENCY TABLE

2. DRAW THE 2. DRAW THE X AND Y AXESX AND Y AXES

HOW TO HOW TO DRAW DRAW

AN OGIVEAN OGIVE

NEXT LESSONNEXT LESSON• QuartileQuartile

• MedianMedian

OGIVEOGIVE

0

5

10

15

20

25

30

35

40

45

50

55

60

65

35 40 45 50 55 60 65 70

Area (cm2)

Cu

mu

lati

ve

fre

qu

en

cy

First Quartile

Median

Third Quartile

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