## 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:

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:

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:

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:

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

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:

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:

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:

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:

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:

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

⇒ 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

⇒ 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:

⇒ 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:

⇒ 5p^{2} + 100p + 295 = 20 (15 + 5p)

⇒ 5p^{2} + 100p + 295 = 300 + 100p

⇒ 5p^{2} + 100p – 100p = 300 – 295

⇒ 5p^{2} = 5 ⇒ p^{2} = \(\frac { 5 }{ 5 }\) = 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.

Solution:

### RD Sharma Class 10 Solutions Chapter 7 Statistics Ex 7.1