## Rajasthan Board RBSE Class 11 Maths Chapter 13 Measures of Dispersion Ex 13.1

Question 1.

Write the formula of quartile deviation.

Solution:

Coefficient of quartile deviation

Here, Q_{3} = upper quartile, Q_{1} = Lower quartile.

Question 2.

For any variable series Q_{1} = 61 and Q_{3} = 121. Find the quartile deviation.

Solution:

Quartile deviation (Q.D.) = \(\frac { { Q }_{ 3 }-{ Q }_{ 1 } }{ 2 } \)

= \(\frac { 121-61 }{ 2 } \)

= \(\frac { 60 }{ 2 } \) = 30.

Question 3.

Find the quartile deviation and coefficient of quartile deviation of the following data.

3, 8, 11, 13, 17, 19, 20, 22, 23, 27, 31

Solution:

Given data is in assending order.

Total number of terms N = 11

Question 4.

Find the range and coefficient of range of the following table –

x | 4.5 | 5.5 | 6.5 | 7.5 | 8.5 | 9.5 | 10.5 | 11.5 |

f | 4 | 5 | 6 | 3 | 2 | 1 | 3 | 5 |

Solution:

Lower limit (S) = 4.5

Upper limit (L)= 11.5

Range = L – S

= 11.5 – 4.5 = 7

Thus range is 7 and coefficient of range is 0.44

Question 5.

Find the inter quartile range and its coefficient for the following series –

X | 1 | 3 | 5 | 7 |

f | 10 | 15 | 3 | 2 |

Solution:

We prepare a table using these datas:

X | f | c.f |

1 | 10 | 10 |

3 | 15 | 25 |

5 | 3 | 28 |

7 | 2 | 30 |

Here, N = 30

Question 6.

Find the coefficient of range of the following data –

Size | 10-15 | 15-20 | 20-25 | 25-30 |

Frequency | 2 | 4 | 6 | 8 |

Solution:

Lower limit (S) = 10

Upper limit (L) = 30

Thus Range coefficient is 0-5.

Question 7.

Find the decile range and percentile range on the basis of following data :

X | f |

0-10 | 3 |

10-20 | 9 |

20-30 | 8 |

30-40 | 5 |

40-50 | 7 |

50-60 | 5 |

60-70 | 7 |

70-80 | 6 |

Solution:

Class (x) |
Frequency (f) |
Cumulative frequency |

0-10 | 3 | 3 |

10-20 | 9 | 12 |

20-30 | 8 | 20 |

30-40 | 5 | 25 |

40-50 | 7 | 32 |

50-60 | 5 | 37 |

60-70 | 7 | 44 |

70-80 | 6 | 50 |

N = 50 |

Calculation of percentile range-

Cumulative frequency exactly greater than 45 is 50, whose corresponding class is 70 – 80

Cumulative frequency exactly greater than 5 is 12, whose corresponding class is 10-20

∴ Percentile range = 71.66 – 12.22 = 59.44

Thus Percentile range = 59.44

Question 8.

Find the decile range and percentile range of the following frequency distribution.

Marks (x) | 0-10 | 10-20 | 20-30 | 30-40 | 40-50 |

Frequency(f) | 5 | 8 | 20 | 14 | 3 |

Solution:

Class (x) | Frequency (f) |
Cumulative frequency |

0-10 | 5 | 5 |

10-20 | 8 | 13 |

20-30 | 20 | 33 |

30-40 | 14 | 47 |

40-50 | 3 | 50 |

N = 30 |

Calculation of Decile Range –

Cumulative frequency exactly greater than 45 is 47, whose corresponding class is 30 – 40

∴ l = 30, f = 14, F = 33, h = 10

Cumulative frequency exactly greater than 5 is 13, whose corresponding class is 10 – 20

∴ l = 10, f = 8, F = 5, h = 10

Cumulative frequency exactly greater than 45 is 47, whose corresponding class is 30 – 40

∴ l = 30, f = 14, F = 33, h = 10

Cumulative frequency exactly greater than 5 is 13, whose corresponding class is 10 – 20

∴ l = 10, f = 8, F = 5, h = 10

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