Question

The sum of all absolute deviation from arithmetic mean for the follwing data is 2,4,6,8,10

Answer 1

SOLUTION

TO DETERMINE

The sum of all absolute deviation from arithmetic mean for the following data is 2 , 4 , 6 , 8 , 10

EVALUATION

Here the given observations are

2 , 4 , 6 , 8 , 10

Sum of the observations

= 2 + 4 + 6 + 8 + 10

= 30

Arithmetic mean

$\displaystyle \sf{ = \frac{30}{5} }$

$\displaystyle \sf{ = 6 }$

Hence the sum of all absolute deviation from arithmetic mean

$\displaystyle \sf{ = \sum _{i = 1}^5 \: |x_i - \bar{x} | }$

$\displaystyle \sf{ = |2 - 6| + |4 - 6| + |6 - 6| + |8 - 6| + |10 - 6| }$

$\displaystyle \sf{ =4 + 2 + 0 + 2 + 4 }$

$\displaystyle \sf{ = 12 }$

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Answer 2

Given :- The sum of all absolute deviation from arithmetic mean for the follwing data is 2,4,6,8,10 ?

Solution :-

→ Arithmetic mean = (2 + 4 + 6 + 8 + 10)/5 = 6

so,

→ sum of all absolute deviation from arithmetic mean = | Mean - xi|

→ sum of all absolute deviation from arithmetic mean = |6 - 2| + |6 - 4| + |6 - 6| + |6 - 8| + |6 - 10| = 4 + 2 + 0 + 2 + 4 = 12 (Ans.)

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