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 and frequency polygon for the following data Class marks 12 . 5 17 . 5 22 . 5 27 . 5 32 . 5 37 . 5 Frequency 7 12 20 28 8 11

We know that 12 . 5 is mid-point of 10 and 15 . Thus, the class intervals can be set as follows in the below table, Class marks Frequency 10 - 15 7 15 - 20 12 20 - 25 20 25 - 30 28 30 - 35 8 35 - 40 11

In a class of 90 students, the marks obtained in a weekly test were as under. Marks 16 - 20 21 - 25 26 - 30 31 - 35 36 - 40 41 - 45 46 - 50 No. of students 4 12 18 26 14 10 6

The given frequency distribution is discontinuous; to convert it into a continuos distribution, Adjustment factor = lower limit of one class - upper limit of previous class 2 = 20 - 21 2 = 1 2 = 0 . 5 Continous frequency distribution for the given data is: Classes before adjustment Classes after adjustments Frequency 16 - 20 15 . 5 - 20 . 5 4 21 - 25 20 . 5 - 25 . 5 12 26 - 30 25 . 5 - 30 . 5 18 31 - 35 30 . 5 - 35 . 5 26 36 - 40 35 . 5 - 40 . 5 14 41 - 45 40 . 5 - 45 . 5 10 46 - 50 45 . 5 - 50 . 5 6 Steps to draw frequency polygon: Since the scale on x - axis starts at 10 . 5 , a kink is shown near the origin on x - axis to indicate that the graph is drawn to scale begining at 10 . 5 . Take 1 cm along x - axis = 5 marks Take 1 cm along y - axis = 4 ( no . of students ) . Find midpoint of class intervals, Find points corresponding to given frequencies of classes and the midpoints of class intervals, and plot them. Join consecutive points by line segments. Join first endpoint with mid-point of class 10 . 5 - 15 . 5 with zero frequency and join the other end with mid-point of class 50 . 5 - 55 . 5 with zero frequency The required frequency polygon is shown below:

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:

The histogram showing the weekly wages (in ₹ ) of workers in a factory is given alongside. What is the class having a minimum frequency?

In the given histogram showing the weekly wages of workers in a factory: The frequency distribution table can be drawn as: Weekly Wages (in ₹ ) Number of workers 375 - 400 6 400 - 425 18 425 - 450 10 450 - 475 20 475 - 500 4 From the above shown table, Class 470 - 500 has the minimum frequency ie. 4 .

M L Aggarwal Solutions for Exercise 3: EXERCISE 20.3

Author:M L Aggarwal

M L Aggarwal Mathematics Solutions for Exercise - M L Aggarwal Solutions for Exercise 3: EXERCISE 20.3

Attempt the practice questions from Exercise 3: EXERCISE 20.3 with hints and solutions to strengthen your understanding. Understanding ICSE Mathematics Class 9 solutions are prepared by Experienced Embibe Experts.

Questions from M L Aggarwal Solutions for Exercise 3: EXERCISE 20.3 with Hints & Solutions

MEDIUM

9th ICSE

IMPORTANT

Understanding ICSE Mathematics Class 9>Chapter 20 - Statistics>EXERCISE 20.3>Q 6

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 ICSE

IMPORTANT

Understanding ICSE Mathematics Class 9>Chapter 20 - Statistics>EXERCISE 20.3>Q 8

Draw a histogram and frequency polygon for the following data

Class marks	$12.5$	$17.5$	$22.5$	$27.5$	$32.5$	$37.5$
Frequency	$7$	$12$	$20$	$28$	$8$	$11$

EASY

9th ICSE

IMPORTANT

Understanding ICSE Mathematics Class 9>Chapter 20 - Statistics>EXERCISE 20.3>Q 13

In a class of 90 students, the marks obtained in a weekly test were as under.

Marks	$16 - 20$	$21 - 25$	$26 - 30$	$31 - 35$	$36 - 40$	$41 - 45$	$46 - 50$
No. of students	$4$	$12$	$18$	$26$	$14$	$10$	$6$

MEDIUM

9th ICSE

IMPORTANT

Understanding ICSE Mathematics Class 9>Chapter 20 - Statistics>EXERCISE 20.3>Q 14

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 ICSE

IMPORTANT

Understanding ICSE Mathematics Class 9>Chapter 20 - Statistics>EXERCISE 20.3>Q 17

The water bills of $32$ houses in a locality are given below:

$30, 48, 52, 78, 103, 85, 37, 94, 72, 73, 66, 52, 92, 65, 78, 81, 64, 60, 75, 78, 108, 63, 71, 54, 59, 75, 100, 103, 35, 89, 95, 73,$

Taking class interval $30 - 40, 40 - 50 . . .$ . from frequency distribution table, construct a combined histogram and frequency polygon.

HARD

9th ICSE

IMPORTANT

Understanding ICSE Mathematics Class 9>Chapter 20 - Statistics>EXERCISE 20.3>Q 18

The number of matchsticks in $40$ boxes on counting was found as given below:

$44, 41, 42, 43, 47, 50, 51, 49, 43, 42, 44, 45, 49, 42, 46, 49, 45, 49, 45, 47, 48, 43, 43, 44, 48, 43, 46, 50, 43, 52, 46, 49, 52, 51, 47, 43, 43, 45 .$

Taking classes $40 - 42, 42 - 44 . .$ construct the frequency distribution table for the above data. Also draw a combined histogram and frequency polygon to represent the distribution.

MEDIUM

9th ICSE

IMPORTANT

Understanding ICSE Mathematics Class 9>Chapter 20 - Statistics>EXERCISE 20.3>Q 19

The histogram showing the weekly wages (in $₹$ ) of workers in a factory is given alongside.

Question Image

What is the frequency of class $400 - 425$ ?

MEDIUM

9th ICSE

IMPORTANT

Understanding ICSE Mathematics Class 9>Chapter 20 - Statistics>EXERCISE 20.3>Q 19

The histogram showing the weekly wages (in $₹$ ) of workers in a factory is given alongside.

Question Image

What is the class having a minimum frequency?

M L Aggarwal Solutions for Exercise 3: EXERCISE 20.3

M L Aggarwal Mathematics Solutions for Exercise - M L Aggarwal Solutions for Exercise 3: EXERCISE 20.3

Questions from M L Aggarwal Solutions for Exercise 3: EXERCISE 20.3 with Hints & Solutions

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