Draw a histogram to represent the following data: Marks obtained 0 - 10 10 - 20 20 - 30 30 - 40 40 - 50 50 - 60 Number of students 4 10 6 8 5 9

Marks obtained 0 - 10 10 - 20 20 - 30 30 - 40 40 - 50 50 - 60 Number of students 4 10 6 8 5 9 Steps to draw histogram: (i) Take 1 cm = 10 marks and plot marks on x -axis and number of students on y -axis. (ii) Take 1 cm = 2 (number of students) (iii) Construct rectangles having their bases as class-width and height as the corresponding frequencies. The required histogram is shown below:

Draw a histogram to represent the following grouped frequency distribution: Age (in years) 20 - 24 25 - 29 30 - 34 35 - 39 40 - 44 45 - 49 50 - 54 Number of teachers 10 28 32 48 50 35 12

Given frequency table is: Age (in years) 20 - 24 25 - 29 30 - 34 35 - 39 40 - 44 45 - 49 50 - 54 Number of teachers 10 28 32 48 50 35 12 The given frequency distribution is discontinuous. To convert into continuous frequency distribution, Adjustment factor = lower limit of one class - upper limit of previous class 2 = 25 - 24 2 = 0 . 5 Subtract the adjustment factor 0 . 5 from all the lower limits and add the adjustment factor 0 . 5 to all the upper limits. Continuous frequency distribution for the given data is: Classes before adjustment Classes after adjustment Frequency 20 - 24 19 . 5 - 24 . 5 10 25 - 29 24 . 5 - 29 . 5 18 30 - 34 29 . 5 - 34 . 5 32 35 - 39 34 . 5 - 39 . 5 48 40 - 44 39 . 5 - 44 . 5 50 45 - 49 44 . 5 - 49 . 5 35 50 - 54 49 . 5 - 54 . 5 12 Steps to draw histogram: (i) Since the scale starts at 19 . 5 , a break is show near the origin. (i) Take 1 cm on x -axis = 5 years and mark the class intervals along x -axis, the end points of which correspond to the class limits. (ii) Take 1 cm on y -axis = 10 teachers and mark the lengths of rectangles along the y -axis. (iii) Construct rectangles having their bases as class-width and height as the corresponding frequencies. The required histogram is shown below:

100 surnames were randomly picked up from a local telephone directory and a frequency distribution of the number of letters in the English alphabet in the surnames was found as follows: Number of letters 1 - 4 4 - 6 6 - 8 8 - 12 12 - 20 Number of surnames 6 30 44 16 4 Draw a histogram to depict the given information. Write the class interval in which the maximum number of surnames lie.

Given frequency table is: Number of letters 1 - 4 4 - 6 6 - 8 8 - 12 12 - 20 Number of surnames 6 30 44 16 4 Here the classes are of unequal size, so it is the case of histogram with varying width. Minimum class size = 2 . Therefore, we are to find the adjusted frequencies to the minimum class size so that these are proportional to the lengths of rectangles of the corresponding class intervals. Adjusted frequency = minimum class size size of class × frequency of the class We prepare the table as under: Number of letters Frequency Width of class Adjusted frequency 1 - 4 6 3 2 3 × 6 = 4 4 - 6 30 2 2 2 × 30 = 30 6 - 8 44 2 2 2 × 44 = 44 8 - 12 16 4 2 4 × 16 = 8 12 - 20 4 8 2 8 × 4 = 1 Steps to draw histogram: (i) Take 1 cm on x -axis = 2 letters and mark the class intervals along x -axis, the end points of which correspond to the class limits. (ii) Take 1 cm on y -axis = 5 surnames and mark the lengths of rectangles along the y -axis. (iii) Construct rectangles having their bases as class-width and height as the corresponding frequencies. The required histogram is shown below: Maximum frequency is 44 . The class interval in which the maximum number of surnames lie is 6 - 8 .

E M B I B E

CBSE Syllabus Standard Mathematics for Class IX>Chapter 14 - Statistics>Exercise 14.3

M L Aggarwal Solutions for Chapter: Statistics, Exercise 3: Exercise 14.3

Author:M L Aggarwal

M L Aggarwal Mathematics Solutions for Exercise - M L Aggarwal Solutions for Chapter: Statistics, Exercise 3: Exercise 14.3

Attempt the practice questions on Chapter 14: Statistics, Exercise 3: Exercise 14.3 with hints and solutions to strengthen your understanding. CBSE Syllabus Standard Mathematics for Class IX solutions are prepared by Experienced Embibe Experts.

Questions from M L Aggarwal Solutions for Chapter: Statistics, Exercise 3: Exercise 14.3 with Hints & Solutions

EASY

9th CBSE

IMPORTANT

CBSE Syllabus Standard Mathematics for Class IX>Chapter 14 - Statistics>Exercise 14.3>Q 1

In the adjoining figure, there is a histogram depicting daily wages of workers in a factory. Construct the frequency distribution table.

Question Image

EASY

9th CBSE

IMPORTANT

CBSE Syllabus Standard Mathematics for Class IX>Chapter 14 - Statistics>Exercise 14.3>Q 2

The frequency distribution has been represented graphically (shown in the adjoining figure). Do you think this representation is correct? Why?

Marks	Number of students
$0 - 20$	$10$
$20 - 40$	$15$
$40 - 60$	$20$
$60 - 100$	$25$

MEDIUM

9th CBSE

IMPORTANT

CBSE Syllabus Standard Mathematics for Class IX>Chapter 14 - Statistics>Exercise 14.3>Q 3

Draw a histogram to represent the following data:

Marks obtained	$0 - 10$	$10 - 20$	$20 - 30$	$30 - 40$	$40 - 50$	$50 - 60$
Number of students	$4$	$10$	$6$	$8$	$5$	$9$

HARD

9th CBSE

IMPORTANT

CBSE Syllabus Standard Mathematics for Class IX>Chapter 14 - Statistics>Exercise 14.3>Q 4

Draw a histogram to represent the following grouped frequency distribution:

Age (in years)	$20 - 24$	$25 - 29$	$30 - 34$	$35 - 39$	$40 - 44$	$45 - 49$	$50 - 54$
Number of teachers	$10$	$28$	$32$	$48$	$50$	$35$	$12$

HARD

9th CBSE

IMPORTANT

CBSE Syllabus Standard Mathematics for Class IX>Chapter 14 - Statistics>Exercise 14.3>Q 5

$100$ surnames were randomly picked up from a local telephone directory and a frequency distribution of the number of letters in the English alphabet in the surnames was found as follows:

Number of letters	$1 - 4$	$4 - 6$	$6 - 8$	$8 - 12$	$12 - 20$
Number of surnames	$6$	$30$	$44$	$16$	$4$

Draw a histogram to depict the given information.

HARD

9th CBSE

IMPORTANT

CBSE Syllabus Standard Mathematics for Class IX>Chapter 14 - Statistics>Exercise 14.3>Q 5

$100$ surnames were randomly picked up from a local telephone directory and a frequency distribution of the number of letters in the English alphabet in the surnames was found as follows: