#### Chapter 24 Measure of Central TendencyÂ R.D. Sharma Solutions for Class 9th Exercise 24.2

**Exercise 24.2**

1.Â Calculate the mean for the following distribution:

x: | 5 | 6 | 7 | 8 | 9 |

f: | 4 | 8 | 14 | 11 | 3 |

**Solution**Â Â

The given distribution in tabulated form isÂ

x: | 5 | 6 | 7 | 8 | 9 |

f: | 4 | 8 | 14 | 11 | 3 |

Prepare the following frequency table of which the first column consists of the values of the variate and the second column the corresponding frequencies. Multiply the frequency of each row with the corresponding values of variable to obtain the third column containing f

_{i}x_{i}.
Â Â

Therefore,

Find the sum of all entries in the second and third column to obtain N and âˆ‘f

_{i}x_{i}Â respectively.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**

The given distribution in tabulated form is

x: | 19 | 21 | 23 | 25 | 27 | 29 | 31 |

f: | 13 | 15 | 16 | 18 | 16 | 15 | 13 |

Prepare the following frequency table of which the first column consists of the values of the variate and the second column the corresponding frequencies. Multiply the frequency of each row with the corresponding values of variable to obtain the third column containing f

_{i}x_{i}.Â
Find the sum of all entries in the second and third column to obtain N and âˆ‘f

_{i}x_{i}Â respectively. Therefore,
3. The mean of the following data is 20.6. Find the value of p

x: | 10 | 15 | p | 25 | 35 |

f: | 3 | 10 | 25 | 7 | 5 |

**Solution**

The given distribution in tabulated form is

x: | 10 | 15 | p | 25 | 35 |

f: | 3 | 10 | 25 | 7 | 5 |

Prepare the following frequency table of which the first column consists of the values of the variate and the second column the corresponding frequencies. Multiply the frequency of each row with the

corresponding values of variable to obtain the third column containing f

_{i}x

_{i}.

_{i}x

_{i}Â respectively. Therefore,

4. If the mean of the following data is 15, find p

x: | 5 | 10 | 15 | 20 | 25 |

f: | 6 | p | 6 | 10 | 5 |

**Solution**Â

The given data in tabulated form is

x: | 5 | 10 | 15 | 20 | 25 |

f: | 6 | p | 6 | 10 | 5 |

_{i}x

_{i}.

_{i}x

_{i}Â respectively. Therefore,

x: | 8 | 12 | 15 | p | 20 | 25 | 30 |

f: | 12 | 16 | 20 | 24 | 16 | 8 | 4 |

**Solution**Â

The given distribution in tabulated form is

x: | 8 | 12 | 15 | p | 20 | 25 | 30 |

f: | 12 | 16 | 20 | 24 | 16 | 8 | 4 |

_{i}x

_{i}Â .

Find the sum of all entries in the second and third column to obtain N and âˆ‘f

_{i}x_{i}Â respectively. Therefore,Â
6. Find the missing value of p for the following distribution whose mean is 12.58.

x: | 5 | 8 | 10 | 12 | p | 20 | 25 |

f: | 2 | 5 | 8 | 22 | 7 | 4 | 2 |

**Solution**

The given distribution in tabulated form is

x: | 5 | 8 | 10 | 12 | p | 20 | 25 |

f: | 2 | 5 | 8 | 22 | 7 | 4 | 2 |

Prepare the following frequency table of which the first column consists of the values of the variate and the second column the corresponding frequencies. Multiply the frequency of each row with the corresponding values of variable to obtain the third column containing f

_{i}x

_{i}.

Find the sum of all entries in the second and third column to obtainÂ

*NÂ*and âˆ‘f

_{i}x

_{i}Â respectively. Therefore,

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**Â

The given distribution in tabulated form is

x: | 3 | 5 | 7 | 9 | 11 | 13 |

f: | 6 | 8 | 15 | p | 8 | 4 |

We have to find the value of p using the information that the mean of the distribution is 7.68. Prepare the following frequency table of which the first column consists of the values of the variate and the second column the corresponding frequencies. Multiply the frequency of each row with the corresponding values of variable to obtain the third column containing f

_{i}x_{i}.
Â

Find the sum of all entries in the second and third column to obtain N and f

_{i}x_{i}Â respectively. Therefore,Â
8. 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**

The given data in tabulated form is

x: | 15 | 17 | 19 | 20+p | 23 |

f: | 2 | 3 | 4 | 5p | 6 |

We have to find the value of p using the information that the mean of the data is 20. Prepare the following frequency table of which the first column consists of the values of the variate and the second column the corresponding frequencies. Multiply the frequency of each row with the corresponding values of variable to obtain the third column containingÂ f

_{i}x

_{i}Â .

_{i}x

_{i}Â respectively. Therefore,

9. Find the mean of the following distribution:

x: | 10 | 12 | 20 | 25 | 35 |

f: | 3 | 10 | 15 | 7 | 5 |

**Solution**Â

The given distribution in tabulated form is

x: | 10 | 12 | 20 | 25 | 35 |

f: | 3 | 10 | 15 | 7 | 5 |

Prepare the following frequency table of which the first column consists of the values of the variate and the second column the corresponding frequencies. Multiply the frequency of each row with the

corresponding values of variable to obtain the third column containing f

_{i}x_{i}. Find the sum of all entries in the second and third column to obtain N and âˆ‘f_{i}x_{i}Â respectively.Â
Find the sum of all entries in the second and third column to obtain N and âˆ‘f

_{i}x_{i}Â respectively. Therefore,Â10. Candidates of four schools appear in a mathematics test. The data were as follows:

**Solution**

Let the number of candidates appeared from school III is p.

Then the given data can be tabulated as

_{i}x

_{i}.

Find the sum of all entries in the second and third column to obtain N andÂ âˆ‘f

_{i}x

_{i}. respectively. Therefore,

11. 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.

**Solution**

The given data can be tabulated in the form

Prepare the following frequency table of which the first column consists of the number of heads and the second column the number of tosses (frequencies). Multiply the frequency of each row with the corresponding number of heads to obtain the third column containing f

_{i}x

_{i}.

Find the sum of all entries in the second and third column to obtainÂ

*N*Â (already given in the question)

*Â*and f

_{i}x

_{i}. respectively. Therefore,

**Solution**

The given distribution in tabulated form is

_{1}Â and f

_{2}, using the information that the mean of the distribution is 50 and the total frequency is 120. Prepare the following frequency table of which the first column consists of the values of the variate and the second column the corresponding frequencies. Multiply the frequency of each row with the corresponding values of variable to obtain the third column containing f

_{i}x

_{i}Â .

_{i}x

_{i}. respectively. Therefore,