Construct the cumulative frequency distribution of the following distribution: Class 12 . 5 - 17 . 5 17 . 5 - 22 . 5 22 . 5 - 27 . 5 27 . 5 - 32 . 5 32 . 5 - 37 . 5 Frequency 2 22 19 14 13

The given distribution is: Class 12 . 5 - 17 . 5 17 . 5 - 22 . 5 22 . 5 - 27 . 5 27 . 5 - 32 . 5 32 . 5 - 37 . 5 Frequency 2 22 19 14 13 We know that there are two types of cumulative frequency distribution: a) Less than type cumulative frequency distribution In 'less than type cumulative frequency', the frequencies of all preceding classes are added to the frequency of that class. b) More than type cumulative frequency distribution In 'more than type cumulative frequency' the frequencies of all succeeding classes are added to the frequency of that class. It is not stated clearly in the question statement which type of the cumulative frequency distribution need to be constructed. Hence, we shall construct both 'less than' and 'more than' type of cumulative frequency distribution: First, we shall construct the 'less than' type cumulative frequency distribution. This is given as under: Class Less than 12 . 5 Less than 17 . 5 Less than 22 . 5 Less than 27 . 5 Less than 32 . 5 Less than 37 . 5 Frequency 0 2 24 43 57 70 Now, we shall construct the 'more than' type cumulative frequency distribution. This is given as under: Class More than 12 . 5 More than 17 . 5 More than 22 . 5 More than 27 . 5 More than 32 . 5 More than 37 . 5 Frequency 70 68 46 27 13 0

Convert the following data into more than type distribution: Class interval 50 - 55 55 - 60 60 - 65 65 - 70 70 - 75 75 - 80 Frequency 2 8 12 24 38 16

We are given to convert the following data into more than type distribution: Class interval 50 - 55 55 - 60 60 - 65 65 - 70 70 - 75 75 - 80 Frequency 2 8 12 24 38 16 We know that in 'more than type cumulative frequency' the frequencies of all succeeding classes are added to the frequency of that class. Hence, the required more than type frequency distribution of the above data is given as under: Class interval More than 50 More than 55 More than 60 More than 65 More than 70 More than 75 More than 80 Frequency 100 98 90 78 54 16 0

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

We are given to find the unknown entries a , b , c , d , e , f in the following distribution of heights of students in a class. Height (in cm ) Frequency Cumulative frequency 150 - 155 12 a 155 - 160 b 25 160 - 165 10 c 165 - 170 d 43 170 - 175 e 48 175 - 180 2 f Total 50 We observe that the numbers in the 'cumulative frequency' column are in the ascending order. Hence, the numbers are arranged as 'less than' type cumulative frequency in the 'cumulative frequency' column. We know that in the 'less than' type cumulative frequency distribution the frequency in each class is obtained by adding successively the frequencies of all the previous classes along with the class against which it is written. Hence, we obtain: a = the same as the frequency of class " 150 - 155 " = 12 b = the cumulative frequency of the class " 155 - 160 " - cumulative frequency of the class " 150 - 155 " = 25 - a = 25 - 12 = 13 c = cumulative frequency of the class " 155 - 160 " + frequency of the class " 160 - 165 " = 25 + 10 = 35 d = cumulative frequency of the class " 165 - 170 " - cumulative frequency of the class " 160 - 165 " = 43 - 35 = 8 e = cumulative frequency of the class " 170 - 175 " - cumulative frequency of the class " 165 - 170 " = 48 - 43 = 5 . f = cumulative frequency of the class " 170 - 175 " + frequency of the class " 175 - 180 " = 48 + 2 = 50 . Hence, the unknown entries are a = 12 , b = 13 , c = 35 , d = 8 , e = 5 and f = 50 . The complete distribution table looks like the following: Height (in cm ) Frequency Cumulative frequency 150 - 155 12 12 a 155 - 160 13 b 25 160 - 165 10 35 c 165 - 170 8 d 43 170 - 175 5 e 48 175 - 180 2 50 f Total 50

Given below is a cumulative frequency distribution showing the marks secured by 50 students of a class: Marks Below 20 Below 40 Below 60 Below 80 Below 100 Number of students 17 22 29 37 50 Form the frequency distribution table for the data.

The given cumulative frequency distribution is: Marks Below 20 Below 40 Below 60 Below 80 Below 100 Number of students 17 22 29 37 50 We observe that the numbers for the "number of students" are in the ascending order. Hence, the distribution is a 'less than' type cumulative frequency distribution. We know that in the 'less than' type cumulative frequency distribution the frequency in each class is obtained by adding successively the frequencies of all the previous classes along with the class against which it is written. Hence, the frequency distribution table derived from the given data is as under: Marks 0 - 20 20 - 40 40 - 60 60 - 80 80 - 100 Number of students 17 5 7 8 13

From the following cumulative frequency table, construct a frequency distribution table: Marks 0 and above 10 and above 20 and above 30 and above 40 and above 50 and above Number of students 40 28 16 10 8 0

The given cumulative frequency distribution is: Marks 0 and above 10 and above 20 and above 30 and above 40 and above 50 and above Number of students 40 28 16 10 8 0 We observe that the numbers for the "number of students" are in descending order. Hence, the distribution is a 'more than' type cumulative frequency distribution. We know that in the 'more than' type cumulative frequency distribution the frequency in each class is obtained by subtracting successively the cumulative frequencies of the succeeding class from the cumulative frequency of that class. Hence, the frequency distribution table derived from the given data is as under: Marks 0 - 10 10 - 20 20 - 30 30 - 40 40 - 50 Number of students 12 12 6 2 8

M L Aggarwal Solutions for Chapter: Statistics, Exercise 3: Exercise 15.3

Author:M L Aggarwal

M L Aggarwal Mathematics Solutions for Exercise - M L Aggarwal Solutions for Chapter: Statistics, Exercise 3: Exercise 15.3

Attempt the practice questions on Chapter 15: Statistics, Exercise 3: Exercise 15.3 with hints and solutions to strengthen your understanding. CBSE Syllabus Standard Mathematics for Class X solutions are prepared by Experienced Embibe Experts.

Questions from M L Aggarwal Solutions for Chapter: Statistics, Exercise 3: Exercise 15.3 with Hints & Solutions

MEDIUM

10th CBSE

IMPORTANT

CBSE Syllabus Standard Mathematics for Class X>Chapter 15 - Statistics>Exercise 15.3>Q 1

Consider the following distribution, find the frequency of the class $30 - 40$ :

Marks obtained	$0$ or more	$10$ or more	$20$ or more	$30$ or more	$40$ or more	$50$ or more
Number of students	$63$	$58$	$55$	$51$	$48$	$42$

MEDIUM

10th CBSE

IMPORTANT

CBSE Syllabus Standard Mathematics for Class X>Chapter 15 - Statistics>Exercise 15.3>Q 2

Construct the cumulative frequency distribution of the following distribution:

Class	$12.5 - 17.5$	$17.5 - 22.5$	$22.5 - 27.5$	$27.5 - 32.5$	$32.5 - 37.5$
Frequency	$2$	$22$	$19$	$14$	$13$

MEDIUM

10th CBSE

IMPORTANT

CBSE Syllabus Standard Mathematics for Class X>Chapter 15 - Statistics>Exercise 15.3>Q 3

Convert the following data into more than type distribution:

Class interval	$50 - 55$	$55 - 60$	$60 - 65$	$65 - 70$	$70 - 75$	$75 - 80$
Frequency	$2$	$8$	$12$	$24$	$38$	$16$

MEDIUM

10th CBSE

IMPORTANT

CBSE Syllabus Standard Mathematics for Class X>Chapter 15 - Statistics>Exercise 15.3>Q 4

Find the unknown entries $a, b, c, d, e, f$ in the following distribution of heights of students in a class:

Height (in $cm$ )	Frequency	Cumulative frequency
$150 - 155$	$12$	$a$
$155 - 160$	$b$	$25$
$160 - 165$	$10$	$c$
$165 - 170$	$d$	$43$
$170 - 175$	$e$	$48$
$175 - 180$	$2$	$f$
Total	$50$

MEDIUM

10th CBSE

IMPORTANT

CBSE Syllabus Standard Mathematics for Class X>Chapter 15 - Statistics>Exercise 15.3>Q 5

Given below is a cumulative frequency distribution showing the marks secured by $50$ students of a class:

Marks	Below $20$	Below $40$	Below $60$	Below $80$	Below $100$
Number of students	$17$	$22$	$29$	$37$	$50$

Form the frequency distribution table for the data.

MEDIUM

10th CBSE

IMPORTANT

CBSE Syllabus Standard Mathematics for Class X>Chapter 15 - Statistics>Exercise 15.3>Q 6

From the following cumulative frequency table, construct a frequency distribution table:

Marks	$0$ and above	$10$ and above	$20$ and above	$30$ and above	$40$ and above	$50$ and above
Number of students	$40$	$28$	$16$	$10$	$8$	$0$

HARD

10th CBSE

IMPORTANT

CBSE Syllabus Standard Mathematics for Class X>Chapter 15 - Statistics>Exercise 15.3>Q 7

Find the mean of the following data:

Class	less than $20$	less than $40$	less than $60$	less than $80$	less than $100$
Frequency	$15$	$37$	$74$	$99$	$120$

HARD

10th CBSE

IMPORTANT

CBSE Syllabus Standard Mathematics for Class X>Chapter 15 - Statistics>Exercise 15.3>Q 8

If the mean age of $100$ residents of a town is $k$ years, find $k$ .

Age equal and above (in years)	$0$	$10$	$20$	$30$	$40$	$50$	$60$	$70$
Number of persons	$100$	$90$	$75$	$50$	$25$	$15$	$5$	$0$

M L Aggarwal Solutions for Chapter: Statistics, Exercise 3: Exercise 15.3

M L Aggarwal Mathematics Solutions for Exercise - M L Aggarwal Solutions for Chapter: Statistics, Exercise 3: Exercise 15.3

Questions from M L Aggarwal Solutions for Chapter: Statistics, Exercise 3: Exercise 15.3 with Hints & Solutions

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