Class 10 RD Sharma Solutions – Chapter 7 Statistics – Exercise 7.2

Question1: The number of telephone calls received at an exchange per interval for 250 successive one-minute intervals are given in the following frequency table:

Number of calls $(x)$	0	1	2	3	4	5	6
Number of intervals $(f)$	15	24	29	46	54	43	39

Compute the mean number of calls per interval.

Solution:

Let the assumed mean(A) be =3 (Generally we choose the middle element to be the assumed mean, but it’s not mandatory),
hence, the table is,

Number of calls $(x_i)$
Number of intervals $(f_i)$
$u_{i}=x_{i}-A=x_{i}-3$
$f_{i}*u_{i}$
0
15
-3
-45
1
24
-2
-48
2
29
-1
-29
3
46
0
0
4
54
1
54
5
43
2
86
6
39
3
117

$\displaystyle\sum_{}^{} f_{i}=250$

$\displaystyle\sum_{}^{} f_{i}*u_{i}=135$
hence, mean of the calls = $A+\frac{\displaystyle\sum_{}^{} f_{i}*u_{i}}{\displaystyle\sum_{}^{} f_{i}}$
= $3+\frac{135}{250}$
= $3.54$
Therefore, mean number of calls per interval is 3.54

Question 2: Five coins were simultaneously tossed 1000 times, and at each toss the number of heads was observed. The number of tosses during which 0, 1, 2, 3, 4, and 5 heads were obtained are shown in the table below. Find the mean number of heads per toss.

Number of heads per toss $(x)$	0	1	2	3	4	5
Number of tosses $(f)$	38	144	342	287	164	25

Solution:

Let the assumed mean (A) be = 2
hence, the table is,
Number of heads per toss $(x_i)$
Number of tosses $(f_i)$
$u_{i}=x_{i}-A=x_{i}-2$
$f_{i}*u_{i}$
0
38
-2
-76
1
144
-1
-144
2
342
0
0
3
287
1
287
4
164
2
328
5
25
3
75

$\displaystyle\sum_{}^{} f_{i}=1000$

$\displaystyle\sum_{}^{} f_{i}*u_{i}=470$
Mean number of head per toss = $A+\frac{\displaystyle\sum_{}^{} f_{i}*u_{i}}{\displaystyle\sum_{}^{} f_{i}}$
= $2+\frac{470}{1000}$
= 2.47
Therefore, mean number of head per toss is 2.47

Question 3: The following table gives the number of branches and number of plants in the garden of a school.

Number of branches $(x)$	2	3	4	5	6
Number of plants $(f)$	49	43	57	38	13

Calculate the average number of branches per plant.

Solution:

Let the assumed mean(A) be = 4
hence, the table is,
Number of branches $(x_i)$
Number of plants $(f_i)$
$u_{i}=x_{i}-A=x_{i}-4$
$f_{i}*u_{i}$
2
49
-2
-98
3
43
-1
-43
4
57
0
0
5
38
1
38
6
13
2
26

$\displaystyle\sum_{}^{} f_{i}=200$

$\displaystyle\sum_{}^{} f_{i}*u_{i}=-77$
Average Number of branches per plant = $A+\frac{\displaystyle\sum_{}^{} f_{i}*u_{i}}{\displaystyle\sum_{}^{} f_{i}}$
= $2+(\frac{-77}{200})$
= 3.615
Therefore, mean number of branches per plant is 3.615

Question 4: The following table gives the number of children of 150 families in a village

Number of children $(x)$	0	1	2	3	4	5
Number of families $(f)$	10	21	55	42	15	7

Find the average number of children per family.

Solution:

Let the assumed mean(A) be = 2
Hence, the table is,
Number of children $(x_i)$
Number of families $(f_i)$
$u_{i}=x_{i}-A=x_{i}-2$
$f_{i}*u_{i}$
0
10
-2
-20
1
21
-1
-21
2
55
0
0
3
42
1
42
4
15
2
30
5
7
3
21

$\displaystyle\sum_{}^{} f_{i}=150$

$\displaystyle\sum_{}^{} f_{i}*u_{i}=52$
Average number of children per family = $A+\frac{\displaystyle\sum_{}^{} f_{i}*u_{i}}{\displaystyle\sum_{}^{} f_{i}}$
= $2+(\frac{52}{150})$
= 2.35 (approximately)
Therefore, the average number of children per family is 2.35 (approximately)

Question 5: The marks obtained out of 50, by 102 students in a Physics test are given in the frequency table below:

Marks $(x)$	15	20	22	24	25	30	33	38	45
Frequency $(f)$	5	8	11	20	23	18	13	3	1

Find the average number of marks.

Solution:

Let the assume mean (A) be = 25
hence, the table is,
Marks $(x_i)$
Frequency $(f_i)$
$u_{i}=x_{i}-A=x_{i}-25$
$f_{i}*u_{i}$
15
5
-10
-50
20
8
-5
-40
22
11
-3
-33
24
20
-1
-20
25
23
0
0
30
18
5
90
33
13
8
104
38
3
13
39
45
1
20
20

$\displaystyle\sum_{}^{} f_{i}=102$

$\displaystyle\sum_{}^{} f_{i}*u_{i}=110$
Average number of marks = $A+\frac{\displaystyle\sum_{}^{} f_{i}*u_{i}}{\displaystyle\sum_{}^{} f_{i}}$
= $25+(\frac{102}{110})$
= 26.08 (approximately)
Therefore, average number of marks is 26.08 (approximately)

Question 6: The number of students absent in a class was recorded every day for 120 days and the information is given in the following

Number of students absent $(x)$	0	1	2	3	4	5	6	7
Number of Days $(f)$	1	4	10	50	34	15	4	2

Find the mean number of students absent per day.

Solution:

Let mean assumed mean (A) be = 3
Number of students absent $(x_i)$
Number of Days $(f)$
$u_{i}=x_{i}-A=x_{i}-3$
$f_{i}*u_{i}$
0
1
-3
-3
1
4
-2
-8
2
10
-1
-10
3
50
0
0
4
34
1
34
5
15
2
30
6
4
3
12
7
2
4
8

$\displaystyle\sum_{}^{} f_{i}=120$

$\displaystyle\sum_{}^{} f_{i}*u_{i}=63$
Mean number of students absent per day = $A+\frac{\displaystyle\sum_{}^{} f_{i}*u_{i}}{\displaystyle\sum_{}^{} f_{i}}$
= $3+(\frac{63}{120})$
= 3.525
Therefore, the mean number of students absent per day is 3.525

Question 7: In the first proof of reading of a book containing 300 pages the following distribution of misprints was obtained:

Number of misprints per page $(x)$	0	1	2	3	4	5
Number of page $(f)$	154	95	36	9	5	1

Find the average number of misprints per page.

Solution:

Let the assumed mean (A) be = 2
Number of misprints per page $(x_i)$
Number of page $(f_i)$
$u_{i}=x_{i}-A=x_{i}-2$
$f_{i}*u_{i}$
0
154
-2
-308
1
95
-1
-95
2
36
0
0
3
9
1
9
4
5
2
10
5
1
3
3

$\displaystyle\sum_{}^{} f_{i}=300$

$\displaystyle\sum_{}^{} f_{i}*u_{i}=-381$
Average number of misprints per day = $A+\frac{\displaystyle\sum_{}^{} f_{i}*u_{i}}{\displaystyle\sum_{}^{} f_{i}}$
= $2+(\frac{-381}{300})$
= 0.73
Therefore, the average number of misprints per day is 0.73

Question 8: Find the mean from the following frequency distribution of marks at a test in statistics:

Number of accidents $(x)$	0	1	2	3	4
Number of workers $(f)$	70	52	34	3	1

Find the average number of misprints per page.

Solution:

Let the assumed mean (A) = 2
Number of accidents $(x_i)$
Number of workers $(f_i)$
$u_{i}=x_{i}-A=x_{i}-2$
$f_{i}*u_{i}$
0
70
-2
-140
1
52
-1
-52
2
34
0
0
3
3
1
3
4
1
2
2

$\displaystyle\sum_{}^{} f_{i}=100$

$\displaystyle\sum_{}^{} f_{i}*u_{i}=-187$
Average no of accidents per day workers = $A+\frac{\displaystyle\sum_{}^{} f_{i}*u_{i}}{\displaystyle\sum_{}^{} f_{i}}$
= $2+(\frac{-187}{100})$
= 0.83
Therefore, average no of accidents per day workers 0.83

Question 9: Find the mean from the following frequency distribution of marks at a test in statistics:

Marks $(x)$	5	10	15	20	25	30	35	40	45	50
Number of students $(f)$	15	50	80	76	72	45	39	9	8	6

Solution:

Let the assumed mean (A) be = 25
Marks $(x_i)$
Number of students $(f_i)$
$u_{i}=x_{i}-A=x_{i}-25$
$f_{i}*u_{i}$
5
15
-20
-300
10
50
-15
-750
15
80
-10
-800
20
76
-5
-380
25
72
0
0
30
45
5
225
35
39
10
390
40
9
15
135
45
8
20
160
50
6
25
150

$\displaystyle\sum_{}^{} f_{i}=400$

$\displaystyle\sum_{}^{} f_{i}*u_{i}=-1170$
Mean = $A+\frac{\displaystyle\sum_{}^{} f_{i}*u_{i}}{\displaystyle\sum_{}^{} f_{i}}$
= $25+(\frac{-1170}{400})$
= 22.075
Therefore, the mean is 22.075

My Personal Notes

Last Updated : 21 Dec, 2020

Related Articles

Class 10 RD Sharma Solutions – Chapter 7 Statistics – Exercise 7.2

Question1: The number of telephone calls received at an exchange per interval for 250 successive one-minute intervals are given in the following frequency table:

Compute the mean number of calls per interval.

Question 2: Five coins were simultaneously tossed 1000 times, and at each toss the number of heads was observed. The number of tosses during which 0, 1, 2, 3, 4, and 5 heads were obtained are shown in the table below. Find the mean number of heads per toss.

Question 3: The following table gives the number of branches and number of plants in the garden of a school.

Calculate the average number of branches per plant.

Question 4: The following table gives the number of children of 150 families in a village

Find the average number of children per family.

Question 5: The marks obtained out of 50, by 102 students in a Physics test are given in the frequency table below:

Find the average number of marks.

Question 6: The number of students absent in a class was recorded every day for 120 days and the information is given in the following

Find the mean number of students absent per day.

Question 7: In the first proof of reading of a book containing 300 pages the following distribution of misprints was obtained:

Find the average number of misprints per page.

Question 8: Find the mean from the following frequency distribution of marks at a test in statistics:

Find the average number of misprints per page.

Question 9: Find the mean from the following frequency distribution of marks at a test in statistics:

CBSE Class 12 Computer Science

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Number of calls $(x_i)$	Number of intervals $(f_i)$	$u_{i}=x_{i}-A=x_{i}-3$	$f_{i}*u_{i}$
0	15	-3	-45
1	24	-2	-48
2	29	-1	-29
3	46	0	0
4	54	1	54
5	43	2	86
6	39	3	117
	$\displaystyle\sum_{}^{} f_{i}=250$		$\displaystyle\sum_{}^{} f_{i}*u_{i}=135$

Number of heads per toss $(x_i)$	Number of tosses $(f_i)$	$u_{i}=x_{i}-A=x_{i}-2$	$f_{i}*u_{i}$
0	38	-2	-76
1	144	-1	-144
2	342	0	0
3	287	1	287
4	164	2	328
5	25	3	75
	$\displaystyle\sum_{}^{} f_{i}=1000$		$\displaystyle\sum_{}^{} f_{i}*u_{i}=470$

Number of branches $(x_i)$	Number of plants $(f_i)$	$u_{i}=x_{i}-A=x_{i}-4$	$f_{i}*u_{i}$
2	49	-2	-98
3	43	-1	-43
4	57	0	0
5	38	1	38
6	13	2	26
	$\displaystyle\sum_{}^{} f_{i}=200$		$\displaystyle\sum_{}^{} f_{i}*u_{i}=-77$

Number of children $(x_i)$	Number of families $(f_i)$	$u_{i}=x_{i}-A=x_{i}-2$	$f_{i}*u_{i}$
0	10	-2	-20
1	21	-1	-21
2	55	0	0
3	42	1	42
4	15	2	30
5	7	3	21
	$\displaystyle\sum_{}^{} f_{i}=150$		$\displaystyle\sum_{}^{} f_{i}*u_{i}=52$

Marks $(x_i)$	Frequency $(f_i)$	$u_{i}=x_{i}-A=x_{i}-25$	$f_{i}*u_{i}$
15	5	-10	-50
20	8	-5	-40
22	11	-3	-33
24	20	-1	-20
25	23	0	0
30	18	5	90
33	13	8	104
38	3	13	39
45	1	20	20
	$\displaystyle\sum_{}^{} f_{i}=102$		$\displaystyle\sum_{}^{} f_{i}*u_{i}=110$

Number of students absent $(x_i)$	Number of Days $(f)$	$u_{i}=x_{i}-A=x_{i}-3$	$f_{i}*u_{i}$
0	1	-3	-3
1	4	-2	-8
2	10	-1	-10
3	50	0	0
4	34	1	34
5	15	2	30
6	4	3	12
7	2	4	8
	$\displaystyle\sum_{}^{} f_{i}=120$		$\displaystyle\sum_{}^{} f_{i}*u_{i}=63$

Number of misprints per page $(x_i)$	Number of page $(f_i)$	$u_{i}=x_{i}-A=x_{i}-2$	$f_{i}*u_{i}$
0	154	-2	-308
1	95	-1	-95
2	36	0	0
3	9	1	9
4	5	2	10
5	1	3	3
	$\displaystyle\sum_{}^{} f_{i}=300$		$\displaystyle\sum_{}^{} f_{i}*u_{i}=-381$

Number of accidents $(x_i)$	Number of workers $(f_i)$	$u_{i}=x_{i}-A=x_{i}-2$	$f_{i}*u_{i}$
0	70	-2	-140
1	52	-1	-52
2	34	0	0
3	3	1	3
4	1	2	2
	$\displaystyle\sum_{}^{} f_{i}=100$		$\displaystyle\sum_{}^{} f_{i}*u_{i}=-187$

Marks $(x_i)$	Number of students $(f_i)$	$u_{i}=x_{i}-A=x_{i}-25$	$f_{i}*u_{i}$
5	15	-20	-300
10	50	-15	-750
15	80	-10	-800
20	76	-5	-380
25	72	0	0
30	45	5	225
35	39	10	390
40	9	15	135
45	8	20	160
50	6	25	150
	$\displaystyle\sum_{}^{} f_{i}=400$		$\displaystyle\sum_{}^{} f_{i}*u_{i}=-1170$

Related Articles

Class 10 RD Sharma Solutions – Chapter 7 Statistics – Exercise 7.2

Question1: The number of telephone calls received at an exchange per interval for 250 successive one-minute intervals are given in the following frequency table:

Compute the mean number of calls per interval.

Question 2: Five coins were simultaneously tossed 1000 times, and at each toss the number of heads was observed. The number of tosses during which 0, 1, 2, 3, 4, and 5 heads were obtained are shown in the table below. Find the mean number of heads per toss.

Question 3: The following table gives the number of branches and number of plants in the garden of a school.

Calculate the average number of branches per plant.

Question 4: The following table gives the number of children of 150 families in a village

Find the average number of children per family.

Question 5: The marks obtained out of 50, by 102 students in a Physics test are given in the frequency table below:

Find the average number of marks.

Question 6: The number of students absent in a class was recorded every day for 120 days and the information is given in the following

Find the mean number of students absent per day.

Question 7: In the first proof of reading of a book containing 300 pages the following distribution of misprints was obtained:

Find the average number of misprints per page.

Question 8: Find the mean from the following frequency distribution of marks at a test in statistics:

Find the average number of misprints per page.

Question 9: Find the mean from the following frequency distribution of marks at a test in statistics:

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CBSE Class 12 Computer Science

GATE CS & IT 2024

Data Structures & Algorithms in JavaScript - Self Paced