TextBook Solutions for Haryana Board - English Medium Class 10 Mathematics Chapter 15 Probability

Question 1

A survey was conducted by a group of students as a part of their environment awareness programme, in which they collected the following data regarding the number of plants in 20 houses in a locality. Find the mean number of plants per house.

Number of plants

Number of houses

0-2

1

2-4

2

4-6

1

6-8

5

8-10

6

10-12

2

12-14

3

Which method did you use for finding the mean and why?

Solution

Number of plants	Number of houses (f_i)	Class mark (x_i)	f_ix_i
0-2	1	1	1
2-4	2	3	6
4-6	1	5	5
6-8	5	7	35
8-10	6	9	54
10-12	2	11	22
12-14	3	13	39
Total	Σf_i = 20		Σf_ix_i = 162

Here, we have

sum from blank to blank of straight f subscript straight i equals 20 comma space sum from blank to blank of straight f subscript straight i straight x subscript straight i

= 162
Now,

top enclose straight x equals fraction numerator begin display style sum from blank to blank of end style f subscript i x subscript i over denominator begin display style sum from blank to blank of end style f subscript i end fraction equals 162 over 2 equals 8.1

Hence, the mean number of plants per house = 8.1
We have used the direct method for finding the mean because numerical values of x_iand f_i are small.

Sponsor Area

Daily wages (in Rs.)	Number of workers
100-120	12
120-140	14
140-160	8
160-180	6
180-200	10

Daily pocket allowance (in Rs.)	11-13	13-15	15-17	17-19	19-21	21-23	23-25
No. of childrens	7	6	9	13	f	5	4

Number of heart beats per minute	65-68	68-71	71-74	74-77	77-80	80-83	83-86
Number of women	2	4	3	8	7	4	2

No. of Mangoes	50-52	53-55	56-58	59-61	62-64
No. of boxes	15	110	135	115	25

Daily Exp. (in Rs.)	100-150	150-200	200-250	250-300	300-350
No. of house hold	4	5	12	2	2

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TextBook Solutions for Haryana Board - English Medium Class 10 Mathematics Chapter 15 Probability

Consider the following distribution of daily wages of 50 workers of a factory:

Daily wages (in Rs.)

Number of workers

100-120

12

120-140

14

140-160

8

160-180

6

180-200

10

Find the mean daily wages of the workers of the factory by using an appropriate method.

The following distribution shows the daily pocket allowance of children of a locality. The mean pocket allowance is Rs. 18. Find the missing frequency 'f'.

Daily pocket allowance (in Rs.)

11-13

13-15

15-17

17-19

19-21

21-23

23-25

No. of childrens

7

6

9

13

f

5

4

The table below shows the daily expenditure on food of 25 household in a locality.

Daily Exp. (in Rs.)

100-150

150-200

200-250

250-300

300-350

No. of house hold

4

5

12

2

2

Find the mean daily expenditure on food by a suitable method.

A class teacher has the following absentee record of 40 students of a class for the whole term. Find the mean number of days a student was absent.

Number of days

0-6

6-10

10-14

14-20

20-28

28-38

38-40

Number of students

11

10

7

4

4

3

1

The following table gives the literacy rate (in percentage) of 35 cities. Find the mean literacy rate.

Literacy rate (in %)

45-55

55-65

65-75

75-85

85-95

Number of cities

3

10

11

8

3

The following table shows the ages of the patients admitted in a hospital during a year.

Find the mode and mean of the data given below. Compare and interpret the measures of central tendency.

Age (in yrs)

No. of patients

5-15

6

15-25

11

25-35

21

35-45

23

45-55

14

55-65

5

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Phone Number

Email Address

Location

Number of plants	Number of houses
0-2	1
2-4	2
4-6	1
6-8	5
8-10	6
10-12	2
12-14	3

Concentration of SO₂ (in ppm)	0.00-0.04	0.04-0.08	0.08-012	0.12-0.16	0.16-0.20	0.20-0.24
Frequencey	4	9	9	2	4	2

Number of days	0-6	6-10	10-14	14-20	20-28	28-38	38-40
Number of students	11	10	7	4	4	3	1

Literacy rate (in %)	45-55	55-65	65-75	75-85	85-95
Number of cities	3	10	11	8	3

Age (in yrs)	No. of patients
5-15	6
15-25	11
25-35	21
35-45	23
45-55	14
55-65	5

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TextBook Solutions for Haryana Board - English Medium Class 10 Mathematics Chapter 15 Probability

Consider the following distribution of daily wages of 50 workers of a factory: Daily wages (in Rs.) Number of workers 100-120 12 120-140 14 140-160 8 160-180 6 180-200 10 Find the mean daily wages of the workers of the factory by using an appropriate method.

The following distribution shows the daily pocket allowance of children of a locality. The mean pocket allowance is Rs. 18. Find the missing frequency 'f'. Daily pocket allowance (in Rs.) 11-13 13-15 15-17 17-19 19-21 21-23 23-25 No. of childrens 7 6 9 13 f 5 4

The table below shows the daily expenditure on food of 25 household in a locality. Daily Exp. (in Rs.) 100-150 150-200 200-250 250-300 300-350 No. of house hold 4 5 12 2 2 Find the mean daily expenditure on food by a suitable method.

A class teacher has the following absentee record of 40 students of a class for the whole term. Find the mean number of days a student was absent. Number of days 0-6 6-10 10-14 14-20 20-28 28-38 38-40 Number of students 11 10 7 4 4 3 1

The following table gives the literacy rate (in percentage) of 35 cities. Find the mean literacy rate. Literacy rate (in %) 45-55 55-65 65-75 75-85 85-95 Number of cities 3 10 11 8 3

The following table shows the ages of the patients admitted in a hospital during a year. Find the mode and mean of the data given below. Compare and interpret the measures of central tendency. Age (in yrs) No. of patients 5-15 6 15-25 11 25-35 21 35-45 23 45-55 14 55-65 5

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Consider the following distribution of daily wages of 50 workers of a factory:

Daily wages (in Rs.)

Number of workers

100-120

12

120-140

14

140-160

8

160-180

6

180-200

10

Find the mean daily wages of the workers of the factory by using an appropriate method.

The following distribution shows the daily pocket allowance of children of a locality. The mean pocket allowance is Rs. 18. Find the missing frequency 'f'.

Daily pocket allowance (in Rs.)

11-13

13-15

15-17

17-19

19-21

21-23

23-25

No. of childrens

7

6

9

13

f

5

4

The table below shows the daily expenditure on food of 25 household in a locality.

Daily Exp. (in Rs.)

100-150

150-200

200-250

250-300

300-350

No. of house hold

4

5

12

2

2

Find the mean daily expenditure on food by a suitable method.

A class teacher has the following absentee record of 40 students of a class for the whole term. Find the mean number of days a student was absent.

Number of days

0-6

6-10

10-14

14-20

20-28

28-38

38-40

Number of students

11

10

7

4

4

3

1

The following table gives the literacy rate (in percentage) of 35 cities. Find the mean literacy rate.

Literacy rate (in %)

45-55

55-65

65-75

75-85

85-95

Number of cities

3

10

11

8

3

The following table shows the ages of the patients admitted in a hospital during a year.

Find the mode and mean of the data given below. Compare and interpret the measures of central tendency.

Age (in yrs)

No. of patients

5-15

6

15-25

11

25-35

21

35-45

23

45-55

14

55-65

5