# Learning Objectives : 6.5 Understand the concept of cumulative frequency.

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Learning Objectives : 6.5 Understand the concept of cumulative frequency

Learning Outcomes: Students will be able for i)Construct the cumulative frequency table for: a) ungrouped data b) grouped data ii)Draw the ogive for: a) ungrouped data b) grouped data Click here

Worksheets 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 frequency table? Ungrouped data Group data. Home

21 1 st card 10 2 nd card 15 3 rd card 12 4 th card 17 5 th card

+ = ? 10 + 21 = 31 21 1 st card 10 2 nd card

+ 31 + = ? + 15 = 46 21 1 st card 10 2 nd card 15 3 rd card

21101512 + + = 46 + 1 st card2 nd card3 rd card 4 th card + 12 = 58 ?

+ + + = ? 78 + 17 = 95 21 1 st card 10 2 nd card 15 3 rd card 12 4 th card 17 5 th card

Ungrouped Data Score01234 Frequency25373 Score Upper boundary Frequency Cumulative Frequency 00.52 11.55 22.53 33.57 44.53 Example 1 2 7 10 17 20

Example 2 : Marks2025303540 Frequency71622132 Marks Upper Boundary Frequency Cumulative Frequency 20 25 30 35 40 Ungrouped Data

Example 2 : Marks2025303540 Frequency71622132 Marks Upper Boundary Frequency Cumulative Frequency 1515.50 2020.57 2525.516 3030.522 3535.513 4040.52 Ungrouped Data 0 7 23 45 58 60

Marks 51- 6061-7071- 8081- 9091-100 Frequency781393 Marks Upper Boundary Frequency Cumulative Frequency 41-5050.50 51-6060.57 61-7070.58 71-8080.513 81-9090.59 91-100100.53 Example 3 : Grouped Data

Exercises Worksheet 1 Worksheet 1 Fill in the tables

Instructions: Constructs the cumulative frequency table base on the table below. Age (year) 1617181920 Frequency2723251619 Worksheet 1

Instructions: Construct the cumulative frequency base on the table below. Volume of petrol (litre) 10-1415-1920-2425-2930-34 Frequency710634 Worksheet 2 Worksheet 2

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6.5 (ii) Draw the ogive for (a) Ungrouped data Home

Height (cm)163164165166167168 Frequency Upper Boundary 165167164165164 168165163164165 ANSWER Table 1: Data of the heights of the basketball players

Height (cm)163164165166167168 Frequency134011 Upper Boundary 163.5164.5165.5166.5167.5168.5 165167164165164 168165163164165 Table 1: Data of the heights of the basketball players

Table 2 : Data of the marks of the students of the Form 4 Cerdik 60758261909198687578 565398686561 706975 568083809975 78 56 Marks51-6061-7071-8081-9091-100 Frequency Upper Boundary ANSWER

Table 2 : Data of the marks of the students of the Form 4 Cerdik 60758261909198687578 565398686561 706975 568083809975 78 56 Marks51-6061-7071-8081-9091-100 Frequency 57 10 34 Upper Boundary 60.5 70.5 80.5 90.5 100.5

The above table shows the frequency of weight of the cakes sold in a shop on a particular day. Using the data given, construct a table of cumulative frequency. Then, draw the ogive with a scale of 2 cm to 1 kg at x-axis and 2 cm to 5 unit at y-axis. Weight of cake (kg) 12345 Frequency461041 EXAMPLE

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 14 26 310 44 51 0.5 1.5 2.5 3.5 4.5 5.5 00 4 10 20 24 25 COMPLETE A TABLE BELOW ADD A CLASS FOR ZERO FREQUENCY BEFORE THE FIRST CLASS

HOW TO DRAW AN OGIVE 1.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 14 26 310 44 51 0.5 1.5 2.5 3.5 4.5 5.5 00 4 10 20 24 25 THE CUMULATIVE FREQUENCY TABLE (Ungrouped data)

5. JOIN ALL THE POINTS SMOOTHLY 4. LABEL THE GRAPH 1. PLOT THE POINTS 3. CONSTRUCT THE CUMULATIVE FREQUENCY TABLE 2. DRAW THE X AND Y AXES 2. DRAW THE X AND Y AXES HOW TO DRAW AN OGIVE

1.52.5 3.5 4.5 5.5 5 10 15 20 25 0.5 Weight of the cakes (kg) x Cumulative Frequency yOgive

Weight of cakes (kg) Upper boundary FrequencyCumulative 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 20 24 25 THE CUMULATIVE FREQUENCY TABLE

Exercises Worksheet 2 Worksheet 2 Fill in the tables Draw the ogives respectively

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Learning Objectives : 6.5 Understand the concept of cumulative frequency

6.1 (ii) Draw the ogive for (b) Grouped data Home

Bar-Chart

Histogram

Frequency Poligon

1.52.5 3.5 4.5 5.5 5 10 15 20 25 0.5 Weight of the cakes (kg) x Cumulative Frequency yOgive

5. JOIN ALL THE POINTS SMOOTHLY 4. LABEL THE GRAPH 3. PLOT THE POINTS 1. CONSTRUCT THE CUMULATIVE FREQUENCY TABLE 2. DRAW THE X AND Y AXES 2. DRAW THE X AND Y AXES HOW TO DRAW AN OGIVE

Step 1 Complete the cumulative frequency table 1.45 1.75 2.05 2.35 2.65 2.95 1.150 6 15 31 36 39 40

Step 2 Draw the scales respectively x-axis : upper boundaries y-axis : Cumulative frequency

Step 3 - plot the points

Step 4 - join the points smoothly

1.52.5 3.5 4.5 5.5 5 10 15 20 25 0.5 Weight of the cakes (kg) x Cumulative Frequency yOgive

Exercises Worksheet 3 Worksheet 3 Fill in the tables Draw the ogives respectively

Table 1 - worksheet 3

Table 2 - worksheet 3

Table 3 - worksheet 3

1.52.5 3.5 4.5 5.5 5 10 15 20 25 0.5 Weight of the cakes (kg) x Cumulative Frequency yOgive

5. JOIN ALL THE POINTS SMOOTHLY 4. LABEL THE GRAPH 1. PLOT THE POINTS 1. PLOT THE POINTS 3. CONSTRUCT THE CUMULATIVE FREQUENCY TABLE 2. DRAW THE X AND Y AXES 2. DRAW THE X AND Y AXES HOW TO DRAW AN OGIVE

NEXT LESSON Quartile Quartile Median Median

OGIVE First Quartile Median Third Quartile

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