Frank Chapter 23 Graphical Representation Solutions Class 10 Maths

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

Answer

(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) 

(v) 

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

Answer

(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

Answer

(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

Answer

(i) 

(ii) 

(iii) 

(iv) 

(v) 

(vi) 

(vii)