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QUESTION: 1

The mean deviation about the mean for the following data:

Solution:

QUESTION: 2

What is the range of the following data?

23, 45, 34, 21, 89, 45, 47, 91

Solution:

Maximum and minimum value of the data 23, 45, 34, 21, 89, 45, 47, 91 are 21 and 91.

Range = 91 – 21 = 70

QUESTION: 3

The mean deviation about the mean for the following data:

Solution:

QUESTION: 4

The mean deviation about the mean for the following data:

Solution:

QUESTION: 5

The mean deviation about the mean for the following data:

5, 6, 7, 8, 6, 9, 13, 12, 15 is:

Solution:

let, X =5,6,7,8,9,13,12,15.

(5+6+7+8+9+13+12+15)÷9 = 9.

and hence a = 9.

the mean deviation about the mean is summation of |X-a|÷ the total number

i.e , |X-a| = 4,3,2,1,3,0,4,3,6 and the total no. is 9.

hence summation of |X-a| = 26,

the mean deviation is 26 ÷ 9 = 2.89 ans

QUESTION: 6

For ungrouped data, mean deviation about mean is =

Solution:

QUESTION: 7

. ……. about a central value ‘a’ is the mean of the absolute values of the deviations of the observations from ‘a’.

Solution:

QUESTION: 8

The mean deviation of the following data 14, 15, 16, 17, 13 is:

Solution:

Here N= 5 , sigma x = 75

so mean = 15

now taking deviation from mean,( By ignoring signs)

we get sigma deviation from mean = 6

Now applying the formula of mean deviation

M.D.= SIGMA deviation from mean/ n

so M.D.= 6/5

= 1.2

QUESTION: 9

The mean deviation about the mean for the following data 3, 7, 8, 9, 4, 6, 8, 13, 12, 10 is:

Solution:

Arrange data in ascending order,

3,4,6,7,8,8,9,10,12,13

No. of observations = 10

Median = n/2 => 10/2 = 5h observation.

5th observation is 8

Now we calculate mean deviation about median, i.e;

=> ∑∣xi−M∣/10

= {|3-8| +|4-8| +|6-8| +|7-8| +|8-8| +|8-8| +|9-8| +|10-8| +|12-8| +|13-8| }/10

= { 5 + 4 + 2 + 1 + 0 + 0 + 1 + 2 + 4 + 5}/10

= 24/10 => 2.4

QUESTION: 10

The arithmetic mean of the numerical values of the deviations of items from some average value is called the

Solution:

Mean deviation of a data set is the average of the absolute deviations from a central point (Average value).

### Mean Deviation (Part - 1)

Video | 12:22 min

### Example: Mean Deviation Method

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### Mean Deviation (Part - 2)

Video | 18:58 min

### Limitation of mean deviation - Statistics

Video | 04:04 min

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