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# Selina Concise Mathematics - Part II Solution for Class 10 Mathematics Chapter 23 - Graphical Representation (Histograms and Ogives)

## Selina Textbook Solutions Chapter 23 - Graphical Representation (Histograms and Ogives)

Selina Textbook Solutions are a perfect way to ace your examination with high marks. These Textbook Solutions are extremely helpful for solving difficult questions in the ICSE Class 10 Mathematics exam. Our Selina Textbook Solutions are written by our subject experts. Find all the answers to the Selina textbook questions of Chapter 23 - Graphical Representation (Histograms and Ogives).

All Selina textbook questions of Chapter 23 - Graphical Representation (Histograms and Ogives) solutions are created in accordance with the latest ICSE syllabus. These free Textbook Solutions for ICSE Class 10 Selina Concise Mathematics will give you a deeper insight on the fundamentals in this chapter and will help you to score more marks in the final examination. ICSE Class 10 students can refer to these solutions while doing their homework and while studying and revising for the Mathematics exam.

Exercise/Page

## Selina Concise Mathematics - Part II Solution for Class 10 Mathematics Chapter 23 - Graphical Representation (Histograms and Ogives) Page/Excercise 23

Solution 1

(i)

 Class Interval Frequency 0-10 12 10-20 20 20-30 26 30-40 18 40-50 10 50-60 06

Steps of construction:

(a) Taking suitable scales, mark class intervals on x-axis and frequency on y-axis.

(b)Construct rectangles with class intervals as bases and corresponding frequencies as heights.

(ii)

 Class Interval Frequency 10-16 15 16-22 23 22-28 30 28-34 20 34-40 16

Steps of construction:

(a) Taking suitable scales, mark class intervals on x-axis and frequency on y-axis.

(b) Construct rectangles with class intervals as bases and corresponding frequencies as heights.

(iii)

 Class Interval (Inclusive form) Class Interval (Exclusive Form) Frequency 30-39 29.5-39.5 24 40-49 39.5-49.5 16 50-59 49.5-59.5 09 60-69 59.5-69.5 15 70-79 69.5-79.5 20

Steps of construction:

(a) Convert the data into exclusive form.

(b) Taking suitable scales, mark class intervals on x-axis and frequency on y-axis.

(c) Construct rectangles with class intervals as bases and corresponding frequencies as heights.

(iv)

 Class Marks Class Intervals Frequency 16 12-20 08 24 20-28 12 32 28-36 15 40 36-44 18 48 44-52 25 56 52-60 19 64 60-68 10

Steps of construction:

(a) Convert the class marks into class intervals.

(b) Taking suitable scales, mark class intervals on x-axis and frequency on y-axis.

(c) Construct rectangles with class intervals as bases and corresponding frequencies as heights.

Solution 2

(i)

 Class Interval Frequency 10-15 10 15-20 15 20-25 17 25-30 12 30-35 10 35-40 08

Steps of construction:

(a) Taking suitable scales, mark class intervals on x-axis and frequency on y-axis.

(b) Construct rectangles with class intervals as bases and corresponding frequencies as heights.

( c) Join the mid-points of the rectangle to obtain the ogive.

(ii)

 Class Interval (Inclusive) Class Interval (Exclusive) Frequency Cumulative Frequency 10-19 9.5-19.5 23 23 20-29 19.5-29.5 16 39 30-39 29.5-39.5 15 54 40-49 39.5-49.5 20 74 50-59 49.5-59.5 12 86 Total 86

Steps of construction:

(a) Convert the data into exclusive form.

(b) Taking suitable scales, mark class intervals on x-axis and frequency on y-axis.

(c) Construct rectangles with class intervals as bases and corresponding frequencies as heights.

(d) Join the mid-points of the rectangle to obtain the ogive.

Solution 3

(i)

 Marks Obtained No. of students (c.f.) less than 10 8 less than 20 25 less than 30 38 less than 40 50 less than 50 67

Steps Of construction:

(a) Plot the points (10,8), (20, 25), (30, 38), (40, 50) and (50, 67) on the graph.

(b) Join them with free hand to obtain an ogive.

(ii)

 Age in years (less than) Cumulative Frequency 10 0 20 17 30 32 40 37 50 53 60 58 70 65

Steps Of construction:

(a) Plot the points (10, 0), (20, 17), (30, 32), (40, 37), (50, 53), (60, 58) and (70, 65) on the graph.

(b) Join them with free hand to obtain an ogive.

Solution 4

(i)

(ii)

Plot the points (30,4), (40,13), (50,22), (60,29), (70,37) and (80,40) on the graph and join them with free hand to obtain an ogive.

Solution 5

(a)

 Class Interval Frequency c.f. 8-12 9 9 12-16 16 25 16-20 22 47 20-24 18 65 24-28 12 77 28-32 4 81

(b) Now plot the points (12, 9), (16, 25), (20, 47), (24, 65), (28, 77), (32, 81) and join them to obtain an ogive.

Solution 6

(a)

Difference in consecutive class marks = 17.5 - 12.5 = 5

first class interval will be 10-15 and so on.

 Class Mark Class Interval Frequency c.f. 12.5 10-15 12 12 17.5 15-20 17 29 22.5 20-25 22 51 27.5 25-30 27 78 32.5 30-35 30 108 37.5 35-40 21 129 42.5 40-45 16 145

Total = 145

(b)

Now plot the points (15,12), (20,29), (25,51), (30,78), (35,108), (40,129), (45,145) and join them to obtain an ogive.

Solution 7

(i)

 Wages No. Of workers c.f. 6500-7000 10 10 7000-7500 18 28 7500-8000 22 50 8000-8500 25 75 8500-9000 17 92 9000-9500 10 102 9500-10000 8 110

Total = 110

Now plot the points (7000,10), (7500,28), (8000,50), (8500,75), (9000,92), (9500,102) and (10000,110) and join them to obtain an ogive.

Solution 8

 Height (in cm) No. Of workers c.f. 150-155 6 6 155-160 12 18 160-165 18 36 165-170 20 56 170-175 13 69 175-180 8 77 180-185 6 83

We plot the points (155, 6), (160, 18), (165, 36), (170, 56), (175, 69),

(180, 77) and (185, 83) on the graph and join them in free hand to obtain an ogive.

Solution 9

(i)

 Marks (less than) Cumulative frequency Frequency 0-10 7 7 10-20 28 28-7=21 20-30 54 54-28=26 30-40 71 71-54=17 40-50 84 84-71=13 50-60 105 105-84=21 60-70 147 147-105=42 70-80 180 180-147=33 80-90 196 196-180=16 90-100 200 200-196=4 Total 200

(ii)

 Marks (more than) Cumulative frequency Frequency 0-10 100 13 10-20 87 22 20-30 65 10 30-40 55 13 40-50 42 6 50-60 36 5 60-70 31 10 70-80 21 3 80-90 18 11 90-100 7 7 Total 100

## Browse Study Material

TopperLearning provides step-by-step solutions for each question in each chapter. Access Chapter 23 - Graphical Representation (Histograms and Ogives)  for ICSE Class 10 Mathematics free of cost. The solutions are provided by our subject matter experts. Refer to our solutions for the Selina Concise Mathematics textbook to revise the whole chapter and clear your fundamentals before the examination. By referring to the solutions for this chapter and the others, we hope that you are able to write your exams well.

# Text Book Solutions

ICSE X - Mathematics

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