# Frank Solutions for Chapter 23 Graphical Representation Class 10 ICSE Mathematics

1. Construct histograms for each of the following frequency distributions:

(i)

 Class Interval 0 – 10 10 – 20 20 – 30 30 – 40 40 – 50 50 – 60 Frequency 8 20 34 22 10 6

(ii)
 Class Interval 130 – 140 140 – 150 150 – 160 160 – 170 170 – 180 Frequency 24 16 29 20 11

(iii)
 Class Interval 1 – 10 11 – 20 21 – 30 31 – 40 41 – 50 Frequency 11 23 30 20 16

(iv)
 Class Interval 110 – 119 120 – 129 130 – 139 140 – 149 150 – 159 Frequency 15 23 30 20 16

(v)

 Class Mark 6 12 18 24 30 36 Frequency 8 12 15 18 25 7

(i) Steps to construct histograms for given frequency distributions,

1. On the x – axis, take 1 cm = 5 units and plot class interval.
2. On the y – axis, take 1 cm = 5 units and plot frequency.
3. Draw rectangles of histograms as per the given frequency distribution.

(ii) Steps to construct histograms for given frequency distributions,

1. On the x – axis, take 1 cm = 5 units and plot class interval.
2. On the y – axis, take 1 cm = 5 units and plot frequency.
3. Draw rectangles of histograms as per the given frequency distribution.

(iii) Steps to construct histograms for given frequency distributions,

1. First we have to make the class intervals continuous by subtracting 0.5 from the lower limit of each class and add 0.5 to the upper limit of each class.

Then we have,

(iv)

2. Construct a histogram and then a frequency polygon for each of the following frequency distribution:

(i)

 Class Interval 0 – 10 10 – 20 20 – 30 30 – 40 40 – 50 50 – 60 Frequency 8 13 27 35 14 3

(ii)

 Class Interval 11 – 20 21 – 30 31 – 40 41 – 50 51 – 60 61 – 70 Frequency 15 28 50 35 20 12
(iii)

 Class Interval 100 – 150 150 – 200 200 – 250 250 – 300 300 – 350 Frequency 10 15 17 12 10

(i)

(ii)

(iii)

3. Construct a frequency polygon without using a histogram for the following frequency distribution:
(i)
 Class Mark 10 15 20 25 30 35 40 Frequency 4 20 40 45 30 25 5
(ii)
 Class Interval 10 – 20 20 – 40 40 – 60 60 – 80 80 – 100 Frequency 9 17 15 20 14
(iii)
 Class Interval 1 – 10 11 – 20 21 – 30 31 – 40 41 – 50 Frequency 8 12 10 16 6
(i)

(ii)

(iii)

4. Draw an ogive for the following:
(i)
 Class Interval 0 – 10 10 – 20 20 – 30 30 – 40 40 – 50 Frequency 8 12 10 14 6
(ii)
 Class Interval 100 – 150 150 – 200 200 – 250 250 – 300 300 – 350 350 – 400 Frequency 10 13 17 12 10 8
(iii)
 Class Interval 10 – 19 20 – 29 30 – 39 40 – 49 50 – 59 Frequency 28 23 15 20 14
(iv)
 Marks Obtained Less than 10 Less than 20 Less than 30 Less than 40 Less than 50 Number of Students 8 22 48 60 75

(v)

 Age in years Less than 10 Less than 20 Less than 30 Less than 40 Less than 50 Number of people 0 17 42 67 100

(vi)

 Marks Obtained More than 10 More than 20 Less than 30 Less than 40 Less than 50 Number of Students 8 25 38 50 67

(vii)

 Marks (more than) 0 10 20 30 40 50 60 70 80 90 100 Cumulative Frequency 100 87 65 55 42 36 31 21 18 7 0