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 $16 t h$ result.

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Solution

Step 1: Find the sum of $31$ results.
$\frac{S u m o f 31 r e s u l t s}{31} = 60$
$S u m o f 31 r e s u l t s = 60 \times 31 = 1860$
Step 2: Find the sum of first $16$ results.
$\frac{S u m o f f i r s t 16 r e s u l t s}{16} = 58$
$S u m o f f i r s t 16 r e s u l t s = 16 \times 58 = 928$
Step 3: Find the sum of last $16$ results.
$\frac{S u m o f l a s t 16 r e s u l t s}{16} = 62$
$S u m o f l a s t 16 r e s u l t s = 16 \times 58 = 992$
Step 4: Find the $16 t h$ result.
$16 t h r e s u l t = s u m o f f i r s t a n d l a s t 16 t h r e s u l t - s u m o f 31 r e s u l t s$
$16 t h r e s u l t = (928 + 992) - (1860)$
$16 t h r e s u l t = (1920) - (1860) = 60$
Hence, the sixteenth result is $60$

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