Learning Objectives : 6.5 Understand the concept of cumulative frequency.
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![Page 1: Learning Objectives : 6.5 Understand the concept of cumulative frequency.](https://reader030.fdocuments.in/reader030/viewer/2022032701/56649c7c5503460f94930ea0/html5/thumbnails/1.jpg)
Learning Objectives :Learning Objectives :
6.5 Understand the concept of6.5 Understand the concept of
cumulative frequencycumulative frequency
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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
Click here
Click here
Click here
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WorksheetsWorksheets• Worksheet 1
• Worksheet 2
• Worksheet 3
•Lesson Plan 1•Lesson Plan 2•Lesson Plan 3
Lesson Plan
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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.
Home
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21211st card
10102nd card
15153rd card
12124th card
17175th card
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+ = ?
10+21 = 31
21211st card
10102nd card
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+
31
+ = ?
+ 15 = 46
21211st card
10102nd card
15153rd card
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2121 1010 1515 1212+ + =
46
+1st card 2nd card 3rd card 4th card
+ 12 = 58
?
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+
+
+ = ?
78 + 17 = 95
21211st card
10102nd card
15153rd card
12124th card
17175th card
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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
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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
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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
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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
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ExercisesExercisesWorksheet 1Worksheet 1
Fill in the tablesFill in the tables
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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
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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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Home
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6.5 (ii) Draw the ogive for6.5 (ii) Draw the ogive for (a) Ungrouped data (a) Ungrouped data
Home
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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
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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
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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
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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
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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
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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
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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
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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
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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)
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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
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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
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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
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ExercisesExercisesWorksheet 2Worksheet 2
Fill in the tablesFill in the tables
Draw the ogives respectivelyDraw the ogives respectively
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Home
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Learning Objectives :Learning Objectives :
6.5 Understand the concept of6.5 Understand the concept of
cumulative frequencycumulative frequency
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6.1 (ii) Draw the ogive for6.1 (ii) Draw the ogive for (b) Grouped data (b) Grouped data
Home
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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ExercisesExercisesWorksheet 3Worksheet 3
Fill in the tablesFill in the tables
Draw the ogives respectivelyDraw the ogives respectively
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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
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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
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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
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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
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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
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NEXT LESSONNEXT LESSON• QuartileQuartile
• MedianMedian
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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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home
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