## Rajasthan Board RBSE Class 11 Maths Chapter 13 Measures of Dispersion Ex 13.3

Find mean and variance for the data of Q. 1. and Q.2

Question 1.

x_{i} |
6 | 10 | 14 | 18 | 24 | 28 | 30 |

f_{i} |
2 | 4 | 7 | 12 | 8 | 4 | 3 |

Solution:

Question 2.

x_{i} |
82 | 83 | 87 | 88 | 92 | 94 | 99 |

f_{i} |
3 | 2 | 3 | 2 | 6 | 3 | 3 |

Solution:

Question 3.

Find mean and standard deviation by shortcut method.

x_{i} |
70 | 71 | 72 | 73 | 74 | 75 | 76 | 77 | 78 |

f_{i} |
2 | 1 | 12 | 29 | 25 | 12 | 10 | 4 | 5 |

Solution:

Let Assumed mean A = 73

Calculation Table

In question 4 and 5, find mean and variable for frequency distribution.

Question 4.

Class | 0-30 | 30-60 | 60-90 | 90-120 | 120-150 | 150-180 | 180-210 |

Frequency | 2 | 3 | 5 | 10 | 3 | 5 | 2 |

Solution:

Calculation table

Question 5.

Class | 0-10 | 10-20 | 20-30 | 30-40 | 40-50 |

Frequency | 5 | 8 | 15 | 16 | 6 |

Solution:

Calculation table

Question 6.

Find mean, variable and standard deviation by short-cut method.

Solution:

Table to find mean, variance, standard deviation :

Question 7.

Find the mean deviation of diameter of circles in given table.

Diameter (mm) | 43-46 | 47-50 | 51-54 | 55-58 | 59-62 |

Number of circles | 15 | 17 | 21 | 22 | 25 |

Solution:

Here groups not continuous. To make it continuous we will subtract 0-5 from lower limit of group and add 0-5 in upper limit.

Calculation table for mean deviation and mean diameter

Thus standard deviation of given circles = 5.55 mm

Question 8.

Calculate standard deviation, its coefficient and variable coefficient of given data.

Class | 0-20 | 20-40 | 40-60 | 60-80 | 80-100 |

Frequency | 2 | 5 | 15 | 7 | 1 |

Solution:

Calculate Table

Question 9.

Find the mean deviation from imaginary mean 35 for following distribution.

35, 25, 33, 50, 37, 35, 33, 37, 30

Solution:

Question 10.

Find mean deviation from mean, median, and mode and coefficient of mean deviation from the following series –

Monthly Wages (in Rs.) | Number of tenants |

Less than 10 | 3 |

Less than 20 | 8 |

Less than 30 | 16 |

Less than 40 | 26 |

Less than 50 | 37 |

Less than 60 | 50 |

Less than 70 | 56 |

Less than 80 | 60 |

Solution:

Cumulative frequency – 1

## Leave a Reply