OP Malhotra Class 10 Maths Solutions Chapter 19 Histogram and Ogive Ex 19(c)

Regular engagement with ICSE Class 10 Maths Solutions S Chand Chapter 19 Histogram and Ogive Ex 19(c) can boost students’ confidence in the subject.

S Chand Class 10 ICSE Maths Solutions Chapter 19 Histogram and Ogive Ex 19(c)

Question 1.
The daily wages of casual labour employed by a group of limited concerns are given below:

Daily wages (in rupees)	3-5	5-7	7-9	9-11	11-13	13-15
Frequency	7	10	23	51	6	3

Draw a cumulative frequency curve for the above data.
Solution:

Daily wages (in Rs.)	Frequency (f)	Cumulative frequency (c.f.)
3-5	7	7
5-7	10	17
7-9	23	40
9-11	51	91
11-13	6	97
13-15	3	100

Now we shall plot the points (5, 7), (7, 17), (9, 40), (11, 91), (13, 97), and (15, 100) on the graph and join them with free hand to get an ogive as shown.

Question 2.
Draw a cumulative frequency curve for the following data :
(a)

Marks	0-10	10-20	20-30	30-40	40-50	50-60
Frequency	5	10	22	40	15	8

(b)

Class interval	0-5	5-10	10-15	15-20	20-25	25-30	30-35	35-40
Frequency	20	23	25	28	30	21	28	16

(c)

Class interval	10-19	20-29	30-39	40-49	50-59	60-69
Frequency	10	15	20	25	30	35

Solution:
(a)

Marks	Frequency	Cumulative frequency
0-10	5	5
10-20	10	15
20-30	22	37
30-40	40	77
40-50	15	92
50-60	8	100

Now we shall plot the points (10, 5), (20, 15), (30, 37), (40, 77), (50, 92) and (60, 100) and join them with free hand to get an ogive as shown.

(b)

Class intervals	Frequency	c.f.
0-5	20	20
5-10	23	43
10-15	25	68
15-20	28	96
20-25	30	126
25-30	21	147
30-35	28	175
35-40	16	191

Now we shall plot the points (5,20), (10,43), (15,68), (20,96), (25,126), (30,147), (35,175) and (40,191) on the graph and join them with free hand to get an ogive as shown :

(c)

Give class interval	Given actual class interval	Frequency	c.f.
10-19	9.5-19.5	10	10
20-29	19.5-29.5	15	25
30-39	29.5-39.5	20	45
40-49	39.5-49.5	25	70
50-59	49.5-59.5	30	100
60-69	595-69.5	35	135

Now we shall plot the points (19.5, 10), (29.5, 25), (39.5, 45), (49.5, 70), (59.5, 100) and (69.5, 135) on the graph and join them with free hand to get an ogive.

Question 3.
Each of the 25 students in a class was given a home assignment comprising 10 questions in mathematics. The data given below show the number of questions solved and submitted by individual students on the next day.
1, 4, 5, 6, 0, 9, 3, 2, 3, 4, 6, 4, 5, 2, 7, 5, 2, 2, 3, 5, 1, 0, 7, 6, 3
(a) Taking classes as 0-2, 2-4, 4-6, etc., make a frequency table for the above distribution.
(b) Draw an Ogive (cumulative frequency curve) to represent the given data.
Solution:

To draw its ogive, we plot the points (2, 7), (4, 12), (6, 19), (8, 24), (10, 25) on the graph and join them with free hand the ogive as shown

Question 4.
Draw an ogive from the following table :

Marks obtained	C.F.
0 and more	100
10 and more	96
20 and more	68
30 and more	26
40 and more	6

Solution:

Marks obtained	c.f.
0-10	100
10-20	96
20-30	68
30-40	26
40-50	6

Now we plot the points (10, 100), (20, 96), (30, 68), (40, 26) and (50, 6) on the graph and join them with free hand to get ogive as shown.

Question 5.
The marks secured by 50 students were as under:

14	12	13	18	11	25	32	27	28	27
3	9	37	31	5	22	13	5	22	14
10	18	40	23	28	19	18	2	13	14
22	7	46	12	36	14	17	19	35	9
12	2	49	43	7	6	10	22	3	27

Taking the size of each class-interval as 10, prepare frequency table and with its help draw a cumulative frequency curve.
Solution:
Highest marks = 49
Lowest marks = 2

Now we shall plot the points (10, 11), (20, 30), (30, 41), (40, 46) and (50, 50) on the graph and join them with free hand to get an ogive as shown.

Question 6.
What is an Ogive curve? How is it useful?
A group of 140 workers in a factory were given a work aptitude test. The distribution of their scores is given below :

Score	No. of Workers	Score	No. of Workers
10-15	2	35-40	19
15-20	7	40-45	27
20-25	9	45-50	20
25-30	15	50-55	11
30-35	26	55-60	4

Draw an Ogive curve.
Solution:
Ogive is a graph of cumulative frequency distribution which is drawn in a free hand curve.

Score	No. of Workers (f)	c.f.
10-15	2	2
15-20	7	9
20-25	9	18
25-30	15	33
30-35	26	59
35-40	19	78
40-45	27	105
45-50	20	125
50-55	11	136
55-60	4	140

Now we shall plot the points (15, 2), (20, 9), (25, 18), (30, 33), (35, 59), (40, 78), (45, 105), (50, 125), (55, 136) and (60, 140) on the graph and join them with free hand to get an ogive as shown.