RD Sharma Class 10 Solutions Chapter 7 Statistics

RD Sharma Class 10 Solutions Statistics Exercise 7.1

Question 1.
Calculate the mean for the following distribution :

X 5 6 7 8 9
f 4 8 14 11 3

Solution:
RD Sharma Class 10 Chapter 7 Statistics

Question 2.
Find the mean of the following data:

X 19 21 23 25 27 29 31
f 13 15 16 18 16 15 13

Solution:
RD Sharma Class 10 Chapter 7 Statistics

Question 3.
If the mean of the following data is 20.6. Find the value of p. (C.B.S.E. 1997)

X 10 15 p 25 35
y 3 10 25 7 5

Solution:
Statistics Class 10 RD Sharma

Question 4.
If the mean of the following data is 15, find p. (C.B.S.E. 1992C)

X 5 10 15 20 25
f 6 P 6 10 5

Solution:
RD Sharma Class 10 Solutions Statistics

Question 5.
Find the value of p for the following distribution whose mean is 16.6.

X 8 12 15 P 20 25 30
f 12 16 20 24 16 8 4

Solution:
Mean = 16.6
RD Sharma Class 10 Solutions Chapter 7 Statistics

Question 6.
Find the missing value of p for the following distribution whose mean is 12.58. (C.B.S.E. 1992C)

X 5 8 10 12 P 20 25
f 2 5 8 22 7 4 2

Solution:
RD Sharma Class 10 Pdf Chapter 7 Statistics

Question 7.
Find the missing frequency (p) for the following distribution whose mean is 7.68.

X 3 5 7 9 11 13
f 6 8 15 P 8 4

Solution:
RD Sharma Solutions Class 10 Chapter 7 Statistics

Question 8.
The following table gives the number of boys of a particular age in a class of 40 students. Calculate the mean age of the students

Age (in years) 15 16 17 18 19 20
No. of students 3 8 10 10 5 4

Solution:
Learncbse.In Class 10 Chapter 7 Statistics

Question 9.
Candidates of four schools appear in a mathematics test. The data were as follows :

Schools No. of Candidates Average Score
I 60 75
II 48 80
III Not available 55
IV 40 50

If the average score of the candidates of all the four schools is 66, find the number of candidates that appeared from school III.
Solution:
Class 10 RD Sharma Solutions Chapter 7 Statistics

Question 10.
Five coins were simultaneously tossed 1000 times and at each toss the number of heads were 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.

No. of heads per toss No. of tosses
0 38
1 144
2 342
3 287
4 164
5 25
Total 1000

Solution:
RD Sharma Class 10 Pdf Free Download Full Book Chapter 7 Statistics

Question 11.
The arithmetic mean of the following data is 14, find the value of k. (C.B.S.E. 2002C)

X 5 10 15 20 25
f 7 k 8 4 5

Solution:
Mean=14
RD Sharma Class 10 Solution Chapter 7 Statistics

⇒ 14 (24 + k) = 360 + 10k
⇒ 336 + 14k = 360 + 10k
⇒ 14k- 10k- 360 -336 24
⇒ 4k = 24
⇒ k= \(\frac { 24 }{ 4 }\) = 6 4
Hence k = 6

Question 12.
The arithmetic mean of the following data is 25, find the value of k. (C.B.S.E. 2001)

X 5 15 25 35 45
f 3 k 3 6 2

Solution:
Mean =25
RD Sharma Class 10 Pdf Ebook Chapter 7 Statistics
⇒ 25 (14 + k) = 390 + 15k
⇒ 350 + 25k= 390 + 15k
⇒ 25k- 15k = 390 -350
⇒ 10k = 40 ⇒ k = \(\frac { 40 }{ 10 }\) = 4
Hence k = 4

Question 13.
If the mean of the following data is 18.75. Find the value of p.

X

10 15 P 25 30
f 5 10 7 8 2

Solution:
RD Sharma Maths Class 10 Solutions Pdf Free Download Chapter 7 Statistics
⇒ 460 + 7p = 32 (18.75)
⇒ 460 + 7p = 600
⇒ 7p = 600 – 460 = 140
⇒ p =  \(\frac { 140 }{ 7 }\) = 20
∴ p = 20

Question 14.
Find the value of p, if the mean of the following distribution is 20.

X 15 17 19 20 + p 23
f 2 3 4 5p 6

Solution:
RD Sharma Class 10 Book Pdf Free Download Chapter 7 Statistics
⇒ 5p2 + 100p + 295 = 20 (15 + 5p)
⇒ 5p2 + 100p + 295 = 300 + 100p
⇒ 5p2 + 100p – 100p = 300 – 295
⇒  5p2 = 5 ⇒  p2  =  \(\frac { 5 }{ 5 }\)  = 1
⇒ P= ±1
P = -1 i s not possible
∴ p= 1

Question 15.
Find the missing frequencies in the following frequency distribution if it is known that the mean of the distribution is 50.
Class 10 RD Sharma Chapter 7 Statistics
Solution:
RD Sharma Maths Class 10 Solutions Chapter 7 Statistics

RD Sharma Class 10 Solutions Chapter 7 Statistics Ex 7.1

RD-Sharma-Class-10-Solutions-Chapter-7-Statistics-Ex-7.1-Q-1
RD-Sharma-Class-10-Solutions-Chapter-7-Statistics-Ex-7.1-Q-2
RD-Sharma-Class-10-Solutions-Chapter-7-Statistics-Ex-7.1-Q-3
RD-Sharma-Class-10-Solutions-Chapter-7-Statistics-Ex-7.1-Q-4
RD-Sharma-Class-10-Solutions-Chapter-7-Statistics-Ex-7.1-Q-5
RD-Sharma-Class-10-Solutions-Chapter-7-Statistics-Ex-7.1-Q-6
RD-Sharma-Class-10-Solutions-Chapter-7-Statistics-Ex-7.1-Q-7
RD-Sharma-Class-10-Solutions-Chapter-7-Statistics-Ex-7.1-Q-8
RD-Sharma-Class-10-Solutions-Chapter-7-Statistics-Ex-7.1-Q-9
RD-Sharma-Class-10-Solutions-Chapter-7-Statistics-Ex-7.1-Q-10
RD-Sharma-Class-10-Solutions-Chapter-7-Statistics-Ex-7.1-Q-11
RD-Sharma-Class-10-Solutions-Chapter-7-Statistics-Ex-7.1-Q-11
RD-Sharma-Class-10-Solutions-Chapter-7-Statistics-Ex-7.1-Q-13
RD-Sharma-Class-10-Solutions-Chapter-7-Statistics-Ex-7.1-Q-14

RD Sharma Class 10 Solutions