Question

If the mean of 11 observations is 17.5 if the one observation is deleted the mean is 16.5 find the deleted observation

Answer 1

$mean \: of \: 11observation \: = 17.5 \\ \\ \frac{sum \: of \: 11obsevation}{total \: number \: of \: observation} = 17.5 \\ \\ \frac{sum \: of \: 11 \: observation}{11} = 17.5 \\ \\ sum \: of \: 11 \: observation \: = 17.5 \times 11 \: = 192.5$

simillarly

sum of 10 observation= 16.5×10 =165

deleted observation = sum of 11 observation -sum of 10 observation

deleted observation = 192.5 -165 =27 .5