In a city, the weekly observations made in a study on the cost of living index are given in the following table: Cost of living index Number of weeks 140 - 150 5 150 - 160 10 160 - 170 20 170 - 180 9 180 - 190 6 190 - 200 2 Total 52 Draw a frequency polygon for the data given above.

We find the class marks and prepare a new table as follows: Cost of living index (Classes) Classes marks Number of weeks (Frequency) 140 - 150 145 5 150 - 160 155 10 160 - 170 165 20 170 - 180 175 9 180 - 190 185 6 190 - 200 195 2 Total 52 Steps to draw frequency polygon: (i) Take 1 cm on x -axis = 10 living index and 1 cm on y -axis = 2 weeks. (ii) Plot the points 145 , 5 , 155 , 10 , 165 , 20 , 175 , 9 , 185 , 6 and 195 , 2 . (iii) Join the consecutive points by line segments. (iv) Join the first end-point with mid-point of class 140 - 150 with zero frequency and join the other end point with the mid-point of class 190 - 200 with zero frequency. The required frequency polygon (thick line segments) is shown below:

100 students in a school have heights as tabulated below: Height (in cm ) Number of students 121 - 130 12 131 - 140 16 141 - 150 30 151 - 160 20 161 - 170 14 171 - 180 8 Draw a frequency polygon of the above data.

The given frequency distribution is discontinuous. To convert into continuous distribution, Adjustment factor = lower limit of one class - upper limit of previous class 2 = 131 - 130 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. Find class marks and prepare the table as under: Classes before adjustment (Height in cm ) Classes after adjustment (Height in cm ) Class marks Number of students 121 - 130 120 . 5 - 130 . 5 125 . 5 12 131 - 140 130 . 5 - 140 . 5 135 . 5 16 141 - 150 140 . 5 - 150 . 5 145 . 5 30 151 - 160 150 . 5 - 160 . 5 155 . 5 20 161 - 170 160 . 5 - 170 . 5 165 . 5 14 171 - 180 170 . 5 - 180 . 5 175 . 5 8 Steps to draw frequency polygon: (i) Take 1 cm on x -axis = 10 cm height and 1 cm on y -axis = 4 students. (ii) Plot the points 125 . 5 , 12 , 135 . 5 , 16 , 145 . 5 , 30 , 155 . 5 , 20 , 165 . 5 , 14 , 175 . 5 , 8 . (iii) Join the consecutive points by thick line segments. (iv) Join the first end-point with mid-point of class 110 . 5 - 120 . 5 with zero frequency and join the other end point with the mid-point of class 180 . 5 - 190 . 5 with zero frequency. The required frequency polygon (thick line segments) is shown below:

Following table shows a frequency distribution for the speed of cars passing through at a particular spot on a highway. Class intervals km / h Frequency 30 - 40 3 40 - 50 6 50 - 60 25 60 - 70 65 70 - 80 50 80 - 90 28 90 - 100 14 Draw a histogram and frequency polygon representing the above data.

We find class marks and prepare the table as under: Class intervals km / h Class marks Frequency 30 - 40 35 3 40 - 50 45 6 50 - 60 55 25 60 - 70 65 65 70 - 80 75 50 80 - 90 85 28 90 - 100 95 14 Steps to draw histogram: (i) Take 1 cm along x -axis = 10 km / h . (ii) Take 1 cm along y -axis = 10 cars (iii) Construct rectangles corresponding to the given data. Steps to draw frequency polygon: (i) Plot the points 35 , 3 , 45 , 6 , 55 , 25 , 65 , 65 , 75 , 50 , 85 , 28 and 95 , 14 . (iii) Join the consecutive points by thick line segments. (iv) Join the first end-point with mid-point of class 20 - 30 with zero frequency and join the other end point with the mid-point of class 100 - 110 with zero frequency. The required frequency polygon (thick line segments) and histogram is shown below:

Following table gives the distribution of students of sections A and B of a class according to the marks obtained by them: Section A Section B Marks Frequency Marks Frequency 0 - 15 5 0 - 15 3 15 - 30 12 15 - 30 16 30 - 45 28 30 - 45 25 45 - 60 30 45 - 60 27 60 - 75 35 60 - 75 40 75 - 90 13 75 - 90 10 Represent the marks of the students of both the sections on the same graph by two frequency polygons. What do you observe?

We find class marks and prepare the table as under: Class Class marks Section A (Number of students) Section B (Number of students) 0 - 15 7 . 5 5 3 15 - 30 22 . 5 12 16 30 - 45 37 . 5 28 25 45 - 60 52 . 5 30 27 60 - 75 67 . 5 35 40 75 - 90 82 . 5 13 10 Steps to draw frequency polygon: Take 1 cm on x -axis = 10 marks and 1 cm on y -axis = 5 students For Section A : Plot the points 7 . 5 , 5 , 22 . 5 , 12 , 37 . 5 , 28 , 52 . 5 , 30 , 67 . 5 , 35 and 82 . 5 , 10 . Join the consecutive points by thick line segments. Join the first end-point with mid-point of class - 15 - 0 with zero frequency and join the other end point with the mid-point of class 90 - 105 . The required frequency polygon is shown by thick line segments in the adjoining figure. For Section B : Plot the points 7 . 5 , 3 , 22 . 5 , 16 , 37 . 5 , 25 , 52 . 5 , 27 , 67 . 5 , 40 and 82 . 5 , 13 . Join the consecutive points by thick line segments. Join the first end-point with mid-point of class - 15 - 0 with zero frequency and join the other end point with the mid-point of class 90 - 105 . The required frequency polygon is shown by dotted line segments in the adjoining figure. The required frequency polygon is shown below: Overall performance of section A is better than performance of section B but more students of section B get higher marks than students of section A .

E M B I B E

CBSE Syllabus Standard Mathematics for Class IX>Chapter 14 - Statistics>Exercise 14.4

M L Aggarwal Solutions for Chapter: Statistics, Exercise 4: Exercise 14.4

Author:M L Aggarwal

M L Aggarwal Mathematics Solutions for Exercise - M L Aggarwal Solutions for Chapter: Statistics, Exercise 4: Exercise 14.4

Attempt the practice questions on Chapter 14: Statistics, Exercise 4: Exercise 14.4 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 4: Exercise 14.4 with Hints & Solutions

MEDIUM

9th CBSE

IMPORTANT

CBSE Syllabus Standard Mathematics for Class IX>Chapter 14 - Statistics>Exercise 14.4>Q 1

In a city, the weekly observations made in a study on the cost of living index are given in the following table:

Cost of living index	Number of weeks
$140 - 150$	$5$
$150 - 160$	$10$
$160 - 170$	$20$
$170 - 180$	$9$
$180 - 190$	$6$
$190 - 200$	$2$
Total	$52$

Draw a frequency polygon for the data given above.

HARD

9th CBSE

IMPORTANT

CBSE Syllabus Standard Mathematics for Class IX>Chapter 14 - Statistics>Exercise 14.4>Q 2

$100$ students in a school have heights as tabulated below:

Height (in $cm$ )	Number of students
$121 - 130$	$12$
$131 - 140$	$16$
$141 - 150$	$30$
$151 - 160$	$20$
$161 - 170$	$14$
$171 - 180$	$8$

Draw a frequency polygon of the above data.

HARD

9th CBSE

IMPORTANT

CBSE Syllabus Standard Mathematics for Class IX>Chapter 14 - Statistics>Exercise 14.4>Q 3

Following table shows a frequency distribution for the speed of cars passing through at a particular spot on a highway.

Class intervals $(km / h)$	Frequency
$30 - 40$	$3$
$40 - 50$	$6$
$50 - 60$	$25$
$60 - 70$	$65$
$70 - 80$	$50$
$80 - 90$	$28$
$90 - 100$	$14$

Draw a histogram and frequency polygon representing the above data.

HARD

9th CBSE

IMPORTANT

CBSE Syllabus Standard Mathematics for Class IX>Chapter 14 - Statistics>Exercise 14.4>Q 4

Following table gives the distribution of students of sections $A$ and $B$ of a class according to the marks obtained by them:

Section $A$		Section $B$
Marks	Frequency	Marks	Frequency
$0 - 15$	$5$	$0 - 15$	$3$
$15 - 30$	$12$	$15 - 30$	$16$
$30 - 45$	$28$	$30 - 45$	$25$
$45 - 60$	$30$	$45 - 60$	$27$
$60 - 75$	$35$	$60 - 75$	$40$
$75 - 90$	$13$	$75 - 90$	$10$