The mean of 31 results is 60. If the mean of the first 16 results is 58 and that of the last 16 results is 62, find the 16th result.

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Solution

Let the total sum of all results be x
now, 60=x/31
x=60×31=1860.
mean of 1st 16 result=58
total sum of 1st 16 results=58×16=928
similarly,total sum of last 16 result=62×16=992
16th number=(928+992-1860)÷2 [since the 16th number is counted twice ]
=60÷2
=30
hence 16th number is 30

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The mean of 31 results is 60. If the mean of the first 16 results is 58 and that of the last 16 results is 62, find the 16th result.

Let the total sum of all results be x now, 60=x/31 x=60×31=1860. mean of 1st 16 result=58 total sum of 1st 16 results=58×16=928 similarly,total sum of last 16 result=62×16=992 16th number=(928+992-1860)÷2 [since the 16th number is counted twice ] =60÷2 =30 hence 16th number is 30

Let the total sum of all results be x
now, 60=x/31
x=60×31=1860.
mean of 1st 16 result=58
total sum of 1st 16 results=58×16=928
similarly,total sum of last 16 result=62×16=992
16th number=(928+992-1860)÷2 [since the 16th number is counted twice ]
=60÷2
=30
hence 16th number is 30