During the medical checkup of 35 students of a class, their weights were recorded as follows. Draw a less than type ogive for the given data.Hence obtained median weight from the graph. Weight (in kg ) No. of students Less than 38 0 Less than 40 3 Less than 42 5 Less than 44 9 Less than 46 14 Less than 48 28 Less than 50 32 Less than 52 35

Less than type cumulative frequency distribution is, Weight (in kg ) Cumulative frequency f i Points 36 - 38 0 ( 38 , 0 ) 38 - 40 3 ( 40 , 3 ) 40 - 42 5 42 , 5 42 - 44 9 ( 44 , 9 ) 44 - 46 14 ( 46 , 14 ) 46 - 48 28 ( 48 , 28 ) 48 - 50 32 ( 50 , 32 ) 50 - 52 35 ( 52 , 35 ) Here, N = 35 , which is odd. So we need to find N 2 which is 35 2 = 17 . 5 . So, the graph we get is, The value N 2 = 17 . 5 is marked on y - axis and a line parallel to x - axis is drawn. This line meets the curve at a point. From that point draw a perpendicular to meet x - axis at median 46 . 5 . Hence, the median of the frequency distribution is 46 . 5 .

Find unknown entries a , b , c , d , e , f in the following distribution of heights of students in class and the total number of students in the class is 50 . Height in cm 150 - 155 155 - 160 160 - 165 165 - 170 170 - 175 175 - 180 Frequency 12 b 10 d e 2 Cumulative frequency a 25 c 43 48 f

The cumulative frequency is calculated by adding each frequency from a frequency distribution table to the sum of its predecessors. Here cumulative frequencies and actual frequencies are given. We need to subtract or add the cumulative frequency to actual frequency to get the values. So, the table we get is Height in cm Frequency Cumulative frequency 150 - 155 12 a = 12 155 - 160 b = 25 - 12 = 13 25 160 - 165 10 c = 25 + 10 = 35 165 - 170 d = 43 - 35 = 8 43 170 - 175 e = 48 - 43 = 5 48 175 - 180 2 f = 48 + 2 = 50 Hence, a = 12 , b = 13 , c = 35 , d = 8 , e = 5 , f = 50 .

Following distribution shows the marks obtained by the class of 100 students. Marks 10 - 20 20 - 30 30 - 40 40 - 50 50 - 60 60 - 70 No. of students 10 15 30 32 8 5 Draw less than ogive for the above data. Find median graphically and verify the result by actual method.

Less than type cumulative frequency distribution is, Marks Cumulative frequency Less than 20 10 Less than 30 25 Less than 40 55 Less than 50 87 Less than 60 95 Less than 70 100 Here, N = 100 . So, N 2 = 50 . Plot the points ( 20 , 10 ) , ( 30 , 25 ) , ( 40 , 55 ) , ( 50 , 87 ) , ( 60 , 95 ) , ( 70 , 100 ) . Join these points to get the required 'less than type ogive' which is as follows: The value N 2 = 50 is marked on y - axis and a line parallel to x - axis is drawn. This line meets the curve at a point. From that point draw a perpendicular to meet x - axis. Hence, the median of the frequency distribution from graph is 38 . 4 . Now by actual method we have, Marks Frequency Cumulative frequency 10 - 20 10 10 20 - 30 15 25 30 - 40 30 55 40 - 50 32 87 50 - 60 8 95 60 - 70 5 100 Here total frequency N = 100 . So, the median class is 30 - 40 as 100 2 = 50 belongs to the cumulative frequency of this class interval. Lower limit of median class l = 30 . Width of the median class interval h = 10 . Total frequency N = 100 . Cumulative frequency preceding median class frequency C = 25 . Frequency of median class f = 30 . Median = l + h N 2 - C f = 30 + 10 50 - 25 30 = 30 + 10 25 30 = 30 + 10 × 5 6 = 30 + 50 6 = 38 . 33 Hence, the median is 38 . 33 ≈ 38 . 34 . So, it is verified by actual method.

H K Dass, Rama Verma and, Bhagwat Swarup Sharma Solutions for Chapter: Statistics, Exercise 7: REVISION EXERCISE

Author:H K Dass, Rama Verma & Bhagwat Swarup Sharma

H K Dass Mathematics Solutions for Exercise - H K Dass, Rama Verma and, Bhagwat Swarup Sharma Solutions for Chapter: Statistics, Exercise 7: REVISION EXERCISE

Attempt the free practice questions on Chapter 14: Statistics, Exercise 7: REVISION EXERCISE with hints and solutions to strengthen your understanding. New Mathematics for Class X solutions are prepared by Experienced Embibe Experts.

Questions from H K Dass, Rama Verma and, Bhagwat Swarup Sharma Solutions for Chapter: Statistics, Exercise 7: REVISION EXERCISE with Hints & Solutions

EASY

10th CBSE

IMPORTANT

New Mathematics for Class X>Chapter 14 - Statistics>REVISION EXERCISE>Q 13

Find the median (upto one decimal place) of the following data:

Marks	$0 - 20$	$20 - 40$	$40 - 60$	$60 - 80$	$80 - 100$
Frequency	$5$	$15$	$30$	$8$	$2$

EASY

10th CBSE

IMPORTANT

New Mathematics for Class X>Chapter 14 - Statistics>REVISION EXERCISE>Q 14

Find the mode (upto two decimal place) of the following distribution of marks obtained by $60$ students.

Marks obtained	$0 - 10$	$10 - 20$	$20 - 30$	$30 - 40$	$40 - 50$
No. of students	$6$	$5$	$12$	$22$	$15$

HARD

10th CBSE

IMPORTANT

New Mathematics for Class X>Chapter 14 - Statistics>REVISION EXERCISE>Q 1

During the medical checkup of $35$ students of a class, their weights were recorded as follows. Draw a less than type ogive for the given data.Hence obtained median weight from the graph.

Weight (in $kg$ )	No. of students
Less than $38$	$0$
Less than $40$	$3$
Less than $42$	$5$
Less than $44$	$9$
Less than $46$	$14$
Less than $48$	$28$
Less than $50$	$32$
Less than $52$	$35$

EASY

10th CBSE

IMPORTANT

New Mathematics for Class X>Chapter 14 - Statistics>REVISION EXERCISE>Q 2

Find unknown entries $a, b, c, d, e, f$ in the following distribution of heights of students in class and the total number of students in the class is $50$ .

Height in cm	$150 - 155$	$155 - 160$	$160 - 165$	$165 - 170$	$170 - 175$	$175 - 180$
Frequency	$12$	$b$	$10$	$d$	$e$	$2$
Cumulative frequency	$a$	$25$	$c$	$43$	$48$	$f$

EASY

10th CBSE

IMPORTANT

New Mathematics for Class X>Chapter 14 - Statistics>REVISION EXERCISE>Q 3

Find the mode of the following frequency distribution:

Marks	$10 - 20$	$20 - 30$	$30 - 40$	$40 - 50$	$50 - 60$	$60 - 70$	$70 - 80$
No. of students	$4$	$8$	$10$	$12$	$10$	$4$	$2$

MEDIUM

10th CBSE

IMPORTANT

New Mathematics for Class X>Chapter 14 - Statistics>REVISION EXERCISE>Q 4

The mean of the following frequency distribution is $54$ . Find the value of $P$ .

Class	$0 - 20$	$20 - 40$	$40 - 60$	$60 - 80$	$80 - 100$
Frequency	$7$	$P$	$10$	$9$	$13$

EASY

10th CBSE

IMPORTANT

New Mathematics for Class X>Chapter 14 - Statistics>REVISION EXERCISE>Q 5

Find the median (upto one decimal place) for the following frequency distribution.

Class interval	$10 - 19$	$20 - 29$	$30 - 39$	$40 - 49$	$50 - 59$	$60 - 69$	$70 - 79$
Frequency	$2$	$4$	$8$	$9$	$4$	$2$	$1$

MEDIUM

10th CBSE

IMPORTANT

New Mathematics for Class X>Chapter 14 - Statistics>REVISION EXERCISE>Q 1

Following distribution shows the marks obtained by the class of $100$ students.

Marks	$10 - 20$	$20 - 30$	$30 - 40$	$40 - 50$	$50 - 60$	$60 - 70$
No. of students	$10$	$15$	$30$	$32$	$8$	$5$

Draw less than ogive for the above data. Find median graphically and verify the result by actual method.

H K Dass, Rama Verma and, Bhagwat Swarup Sharma Solutions for Chapter: Statistics, Exercise 7: REVISION EXERCISE

H K Dass Mathematics Solutions for Exercise - H K Dass, Rama Verma and, Bhagwat Swarup Sharma Solutions for Chapter: Statistics, Exercise 7: REVISION EXERCISE

Questions from H K Dass, Rama Verma and, Bhagwat Swarup Sharma Solutions for Chapter: Statistics, Exercise 7: REVISION EXERCISE with Hints & Solutions

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