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Question

The mean of 5 numbers is 18. If one number is excluded, their mean is 16. Find the excluded number.


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Solution

Step 1: Find the value of sum of terms

Given, the mean of five numbers items is X¯=18.

MeanX¯=SumoftermsNumberofterms

18=x1+x2+x3+x4+x55

90=x1+x2+x3+x4+x5

Step 2: Find the new value of sum of terms, if one of the numbers is excluded.

Let excluded number=x5

Sumofnumbers=x1+x2+x3+x4

=90-x5

Step 3: Find the excluded number.

Given, the mean of the remaining numbers is 16. Which means the mean of four numbers is 16.

I.e.,

MeanX¯=SumoftermsNumberofterms

16=90-x54

90-x5=64

x5=90-64

x5=26

Hence, the value of excluded number is 26.


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