using a graph paper, draw an Ogive for the folowing distribution which shows a record of the weight in kilograms of 200 students. Weight 40 - 50 45 - 50 50 - 55 55 - 60 60 - 65 65 - 70 70 - 75 75 - 80 Frequency 5 17 22 45 51 31 20 9 Use Ogive to estimate the following : The percentage of students weighing 55 kg OR more,

Weight frequency Cumulative frequency ( c . f ) 40 - 45 5 5 45 - 50 17 22 50 - 55 22 44 55 - 60 45 89 60 - 65 51 140 65 - 70 31 171 70 - 75 20 191 75 - 80 9 200 Students more than 55 = 200 - 44 = 156 % = 56 200 × 100 = 78 % The cumulative frequency is calculated by adding each frequency from a frequency distribution table to the sum of its predecessors.

using a graph paper, draw an Ogive for the folowing distribution which shows a record of the weight in kilograms of 200 students. Weight 40 - 50 45 - 50 50 - 55 55 - 60 60 - 65 65 - 70 70 - 75 75 - 80 Frequency 5 17 22 45 51 31 20 9 Use Ogive to estimate the following : The weight above which the heaviest 30 % of the students fall,

Weight frequency Cumulative frequency ( c . f ) 40 - 45 5 5 45 - 50 17 22 50 - 55 22 44 55 - 60 45 89 60 - 65 51 140 65 - 70 31 171 70 - 75 20 191 75 - 80 9 200 30 % students = 30 × 200 100 = 60 Heaviest 60 students in weight 9 + 21 + 30 = 60 weight = 65 Kg The cumulative frequency is calculated by adding each frequency from a frequency distribution table to the sum of its predecessors.

Using a graph paper, draw an Ogive for the following distribution which shows a record of the weight in kilograms of 200 students. Weight 40 - 50 45 - 50 50 - 55 55 - 60 60 - 65 65 - 70 70 - 75 75 - 80 Frequency 5 17 22 45 51 31 20 9 Use Ogive to estimate the following: The number of students who are (a) under-weight and (b) over-weight, if 55 - 70 kg is considered as standard weight?

Weight frequency Cumulative frequency ( c . f ) 40 - 45 5 5 45 - 50 17 22 50 - 55 22 44 55 - 60 45 89 60 - 65 51 140 65 - 70 31 171 70 - 75 20 191 75 - 80 9 200 students underweight when 55 . 70 Kg is standard = 46 overweight student when 55 . 70 Kg is standard = 200 - 55 . 70 = 154 Cumulative frequency analysis is the analysis of the frequency of occurrence of values of a phenomenon less than a reference value. The phenomenon may be time- or space-dependent. Cumulative frequency is also called frequency of non-exceedance.

The mean of the following distribution is 52 and the frequency of class interval 30 - 40 is ' f ' . Find ' f ' . Class Interval 10 - 20 20 - 30 30 - 40 40 - 50 50 - 60 60 - 70 70 - 80 Frequency 5 3 f 7 2 6 13

Class Interval frequency ( f ) Mid value ( x ) f x 10 - 20 5 15 75 20 - 30 3 25 75 30 - 40 f 35 35 f 40 - 50 7 45 315 50 - 60 2 55 140 60 - 70 6 65 390 70 - 80 13 75 975 Total 36 + f 1940 + 35 f Mean = 52 Mean = ∑ f x ∑ f 52 = 1940 + 35 f 36 + f 17 f = 64 f = 4

HARD

10th ICSE

IMPORTANT

Earn 100

The marks obtained by $20$ students in Mathematics test are given below:

Marks $0 - 10$ $10 - 20$ $20 - 30$ $30 - 40$ $40 - 50$ $50 - 60$ $60 - 70$ $70 - 80$ $80 - 90$ $90 - 100$

No.of students $5$ $9$ $16$ $22$ $26$ $18$ $11$ $6$ $4$ $3$

Draw an ogive for the given distribution on a graph sheet. Use a suitable scale for your ogive.Use your ogive to estimate:

The number of students who obtained more than $75 %$ marks in a test?

Important Questions on Measures of Central Tendency (Mean, Median, Quartiles and Mode)

HARD

10th ICSE

IMPORTANT

Concise Mathematics>Chapter 24 - Measures of Central Tendency (Mean, Median, Quartiles and Mode)>EXERCISE>Q 7

The marks obtained by $20$ students in Mathematics test are given below:

Marks	$0 - 10$	$10 - 20$	$20 - 30$	$30 - 40$	$40 - 50$	$50 - 60$	$60 - 70$	$70 - 80$	$80 - 90$	$90 - 100$
No.of students	$5$	$9$	$16$	$22$	$26$	$18$	$11$	$6$	$4$	$3$

Draw an ogive for the given distribution on a graph sheet. Use a suitable scale for your ogive.Use your ogive to estimate:

The number of students who did not pass in the test if the pass percentage was $40$ ?

HARD

10th ICSE

IMPORTANT

Concise Mathematics>Chapter 24 - Measures of Central Tendency (Mean, Median, Quartiles and Mode)>EXERCISE>Q 7

The marks obtained by $20$ students in Mathematics test are given below:

Marks	$0 - 10$	$10 - 20$	$20 - 30$	$30 - 40$	$40 - 50$	$50 - 60$	$60 - 70$	$70 - 80$	$80 - 90$	$90 - 100$
No.of students	$5$	$9$	$16$	$22$	$26$	$18$	$11$	$6$	$4$	$3$

Draw an ogive for the given distribution on a graph sheet. Use a suitable scale for your ogive. Use your ogive to estimate:

The lower quartile.

HARD

10th ICSE

IMPORTANT

Concise Mathematics>Chapter 24 - Measures of Central Tendency (Mean, Median, Quartiles and Mode)>EXERCISE>Q 8

using a graph paper, draw an Ogive for the folowing distribution which shows a record of the weight in kilograms of $200$ students.

Weight	$40 - 50$	$45 - 50$	$50 - 55$	$55 - 60$	$60 - 65$	$65 - 70$	$70 - 75$	$75 - 80$
Frequency	$5$	$17$	$22$	$45$	$51$	$31$	$20$	$9$

Use Ogive to estimate the following :

The percentage of students weighing $55 kg$ OR more,

HARD

10th ICSE

IMPORTANT

Concise Mathematics>Chapter 24 - Measures of Central Tendency (Mean, Median, Quartiles and Mode)>EXERCISE>Q 8

using a graph paper, draw an Ogive for the folowing distribution which shows a record of the weight in kilograms of $200$ students.

Weight	$40 - 50$	$45 - 50$	$50 - 55$	$55 - 60$	$60 - 65$	$65 - 70$	$70 - 75$	$75 - 80$
Frequency	$5$	$17$	$22$	$45$	$51$	$31$	$20$	$9$

Use Ogive to estimate the following :

The weight above which the heaviest $30 %$ of the students fall,

HARD

10th ICSE

IMPORTANT

Concise Mathematics>Chapter 24 - Measures of Central Tendency (Mean, Median, Quartiles and Mode)>EXERCISE>Q 8

Using a graph paper, draw an Ogive for the following distribution which shows a record of the weight in kilograms of $200$ students.

Weight	$40 - 50$	$45 - 50$	$50 - 55$	$55 - 60$	$60 - 65$	$65 - 70$	$70 - 75$	$75 - 80$
Frequency	$5$	$17$	$22$	$45$	$51$	$31$	$20$	$9$

Use Ogive to estimate the following:

The number of students who are (a) under-weight and (b) over-weight, if $55 - 70 kg$ is considered as standard weight?

HARD

10th ICSE

IMPORTANT

Concise Mathematics>Chapter 24 - Measures of Central Tendency (Mean, Median, Quartiles and Mode)>EXERCISE>Q 9

the distribution, given below, shows the marks obtained by $25$ students in an aptitude test. Find the mean, median and mode of distribution.

Marks obtained	$5$	$6$	$7$	$8$	$9$	$10$
Number of students	$3$	$9$	$6$	$4$	$2$	$1$

MEDIUM

10th ICSE

IMPORTANT

Concise Mathematics>Chapter 24 - Measures of Central Tendency (Mean, Median, Quartiles and Mode)>EXERCISE>Q 10

The mean of the following distribution is $52$ and the frequency of class interval $30 - 40$ is $' f' .$ Find $' f' .$

Class Interval	$10 - 20$	$20 - 30$	$30 - 40$	$40 - 50$	$50 - 60$	$60 - 70$	$70 - 80$
Frequency	$5$	$3$	$f$	$7$	$2$	$6$	$13$

HARD

10th ICSE

IMPORTANT

Concise Mathematics>Chapter 24 - Measures of Central Tendency (Mean, Median, Quartiles and Mode)>EXERCISE>Q 11

The monthly income of a group of $320$ employees in a company is given below:

Monthly Income

[in thousands]

6 - 7

7 - 8

8 - 9

9 - 10

10 - 11

11 - 12

12 - 13

No.of Employees

20

45

65

95

60

30

5

Draw an ogive of the given distribution on a graph sheet taking $2 cm = ₹ 1000$ on one axis and $2 cm = 50$ employees on the other axis. From the graph determine:

The median wage.

Important Questions on Measures of Central Tendency (Mean, Median, Quartiles and Mode)

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