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#### The mean of 5 observations is 5 and their variance is 124.  If three of the observations are 1, 2 and 6 ; then the mean deviation from the mean of the data is : Option 1) 2.4 Option 2) 2.8 Option 3) 2.5 Option 4) 2.6

Initially, we need to look at the following concepts:

ARITHMETIC Mean -

For the values x1, x2, ....xn of the variant x the arithmetic mean is given by

in case of discrete data.

-

Mean Deviation -

If x1, x2, ...xn are n observations then the mean deviation from the point A is given by :

-

Variance -

In case of discrete data

-

Now,

Let the two observations be a & b

a+b+1+2+6=25

a+b=16

a2+b2+12+22+62=745

a2+b2+1+4+36=745

a2+b2=704

Option 1)

2.4

This option is incorrect.

Option 2)

2.8

This option is correct.

Option 3)

2.5

This option is incorrect.

Option 4)

2.6

This option is incorrect.
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