Question

The mean of 18 observation is 13. If one of the
observation 25 is excluded from the group, what is
the new mean?​

Answer 1

Let the elements be, x1,x2,x3....X18

Mean= total sum of elements/ total no. of elements.

=> Given mean is = 13 of 18 elements,

=>13= X1+x2+...x18/18

=> 234=x1+x2+ ... x18

Excluding one let it be x18, it is 28,

so, Sum of remaining is.

=> 234-25

=> 209

Therefore,Now.

=>( x1+x2+...+x17)/17 = mean

=> 209/17= new mean=12.29

So the new mean after removal of 25 is 12.29 .

Ans.

Answer 2

Given :-

• Mean of 18 observation = 13.
• Excluded Number = 25
• New Mean = ?

Solution :-

→ Mean = (Sum of Observation) / (Total Number of Observation).

Putting Values :-

→ 13 = (sum of observation) / 18

→ 13 * 18 = sum of observation

→ sum of observation = 234 .

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Now, 25 is Excluded From Group.

So,

→ New Sum of observation = 234 - 25 = 209.

→ Total Number of Observation Now = 18 - 1 = 17.

So,

→ New Mean = (209/17)

→ New Mean = 12.28 (Ans).

Hence ,New Average will be 12.28 .

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Shortcut :-

→ New Average = Old Average - ( Total Number of Observation / Excluded Number ).

Putting Values :-

→ New Average = 13 - (18/25)

→ New Average = 13 - 0.72

→ New Average = 12.28 (Ans).

Hence, New Average will be 12.28.

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