Question

The mean of six numbers is 20. If one of the numbers is excluded, the average is 8. Find out
the excluded number.
A. 12
B. 22
C. 80
D. 120​

Answer 1

Mean of six terms = 20

$\rm \longrightarrow \dfrac{x_1 + x_2 + x_3...x_6}{6} = 20 \\ \\ \rm \longrightarrow {x_1 + x_2 + x_3...x_6} = 20 \times 6\\ \\ \rm \longrightarrow {x_1 + x_2 + x_3...x_6} = 120$

$\rm \longrightarrow {x_1 + x_2 + x_3...x_6} =s_a = 120$

If one of the numbers is excluded, the average is = 8

$\rm \longrightarrow \dfrac{x_1 + x_2 + x_3...x_5}{5} = 8 \\ \\ \rm \longrightarrow {x_1 + x_2 + x_3...x_5} = 8 \times 5\\ \\ \rm \longrightarrow {x_1 + x_2 + x_3...x_5} =40$

$\rm \longrightarrow {x_1 + x_2 + x_3...x_5} =s_ b=40$

$\rm \longrightarrow Excluded \: number = s_ a -s_ b \\ \\ \rm \longrightarrow Excluded \: number = 120 -40\\ \\ \rm \longrightarrow Excluded \: number = 80$

Therefore, option (c) 80 is correct

Answer 2

Given :-

The mean of six numbers is 20. If one of the numbers is excluded, the average is 8.  

To Find :-

Excluded number

Solution :-

We know that

Mean = Sum of observation/Total no. of observation

Mean × Total no. of observation =  Sum of observation

20 × 6 = Sum of observation

120 = Sum of observation

One number is excluded. It means one number has been removed from the set

So, Total observation = 6 - 1 = 5

Mean = Sum of observation/Total no. of observation

Mean × Total no. of observation = Sum of observation

8 × 5 = Sum of observation

40 = Sum of observation

Excluded number = Old sum of observation - New sum of observation

Excluded number = 120 - 40

Excluded number = 80

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