## Rajasthan Board RBSE Class 11 Maths Chapter 13 Measures of Dispersion Ex 13.2

Find the mean deviation from mean for the data given in Q1 and Q2.

Question 1.

4, 7, 8, 9, 10, 12, 13,17

Solution:

Question 2.

28, 60, 38,30, 32, 45, 53, 36,44, 34

Solution:

Find the mean deviation from median for the data given in Q. 3 and Q.4.

Question 3.

13,10, 12,13, 15, 18, 17, 11,14,16, 12

Solution:

Arranging is ascending order, value of varaible will be

10, 11, 12, 12, 13, 13, 14, 15, 16, 17, 18

Here n = 11

? Median (M) = Mean of values of 5th and 6th term

M = \(\frac { 13+13 }{ 2 } \) = \(\frac { 26 }{ 2 } \) = 13

x_{i} |
| x_{i} – m| |

13 | 0 |

10 | 3 |

12 | 1 |

13 | 0 |

15 | 2 |

18 | 5 |

17 | 4 |

11 | 2 |

14 | 1 |

16 | 3 |

12 | 1 |

N = 11 | ∑ | x_{i} – m | = 22 |

Mean deviation from median

Question 4.

26, 32, 35, 39, 41, 62, 36, 50, 43.

Solution:

Arranging in ascending order, value of variable will be

26, 32, 35, 36, 39, 41, 43, 50, 62

Here number of total terms

N = 9

Table for calcuation of Mean deviation

Find the mean deviation from mode for the data given in Q. 5. and Q. 6.

Question 5.

2, 4, 6, 4, 8, 6, 4, 10, 4, 8

Solution:

Maximum time (4 times) in given data, 4 ocurs

Now, Mode (z) = 4

x_{i} |
|x_{i} – z | |

2 | 2 |

4 | 0 |

6 | 2 |

4 | 0 |

8 | 4 |

6 | 2 |

4 | 0 |

10 | 6 |

4 | 0 |

8 | 4 |

N = 10 |
∑ | x_{i} – z | = 20 |

Thus, Mean deviation from mode,

Question 6.

2.2, 2.5, 2.1, 2.5, 2.9, 2.8, 2.5, 2.3

Solution:

In given data 2-5 occurs maximum times (3 times)

Thus Mode (z) = 2.5

x_{i} |
2.2 | 2.5 | 2.1 | 2.5 | 2.9 | 2.8 | 2.5 | 2.3 |
N = 8 |

| x_{i} – z | |
0.3 | 0 | 0.4 | 0 | 0.4 | 0.3 | 0 | 0.2 | ∑ |x_{i} – z| = 1-6 |

Thus Mean deviation (δz) about mode

Find the mean deviation from mean for the data given in Q. 7 to Q. 8.

Question 7.

x_{i} |
5 | 10 | 15 | 20 | 25 |

f_{i} |
7 | 4 | 6 | 3 | 5 |

Solution:

Calculation table for mean deviation about mean

Question 8.

x_{i} |
20 | 40 | 60 | 80 | 100 |

f_{i} |
2 | 12 | 14 | 8 | 4 |

Solution:

Calculation table for mean deviation from mean.

Find the mean deviation from median for the data given in Q. 9. and Q. 10.

Question 9.

x_{i} |
5 | 7 | 9 | 10 | 12 | 15 |

f_{i} |
8 | 6 | 2 | 2 | 2 | 6 |

Solution:

Question 10.

^{xi} |
10 | 16 | 22 | 25 | 30 |

f_{i} |
3 | 5 | 6 | 7 | 8 |

Solution:

Find the mean deviation from mode for data given in Q. 11 to Q. 12.

Question 11.

x_{i} |
3 | 4 | 5 | 6 | 7 | 8 |

f_{i} |
2 | 4 | 6 | 3 | 2 | 1 |

Solution:

Question 12.

x_{i} |
10 | 20 | 30 | 40 | 50 | 60 | 70 | 80 |

f_{i} |
2 | 8 | 16 | 26 | 20 | 16 | 7 | 5 |

Solution:

Find the mean deviation from mean for data given in Q. 13. and Q. 14.

Question 13.

Income(daily) | Number |

0-10 | 4 |

10-20 | 8 |

20-30 | 9 |

30-40 | 10 |

40-50 | 7 |

50-60 | 5 |

60-70 | 4 |

70-80 | 3 |

Solution:

Question 14.

Height (cm) |
95-105 | 105-115 | 115-125 | 125-135 | 135-145 | 145-155 |

Number | 9 | 13 | 26 | 30 | 12 | 10 |

Solution:

Find the mean deviation from median for data given in Q. 15. and Q. 16.

Question 15.

Marks | Number |

10-20 | 3 |

20-30 | 4 |

30-40 | 7 |

40-50 | 8 |

50-60 | 2 |

60-70 | 1 |

Solution:

Question 16.

Age | Number |

16-20 | 5 |

21-25 | 6 |

26-30 | 12 |

31-35 | 14 |

36-40 | 26 |

41-45 | 12 |

46-50 | 16 |

51-55 | 9 |

Solution:

Find the mean deviation from mode for data given in Q. 17 and Q. 18.

Question 17.

Class | 20-30 | 30-40 | 40-50 | 50-60 | 60-70 |

Number | 8 | 24 | 42 | 20 | 6 |

Solution:

Question 18.

Height (Inches) |
52-55 | 55-58 | 58-61 | 61-64 |

No. of Students | 10 | 20 | 35 | 10 |

Solution:

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