Question

The calculated mean of 50 observations was 80. It was later discovered that observation 19 was recorded by mistake as 91. What Was the correct mean?

Answer 1

Here, mean = 80, number of observations = 50 

\(Mean = \cfrac{The\,sum \,of\, all \,observatiojns \,in \,the \,data }{Total \,number \,of \,observations}\)

∴ The sum of all observations = Mean x Total number of observations 

∴ The sum of 50 observations = 80 x 50 = 4000 

One of the observation was 19. However, by mistake it was recorded as 91. 

Sum of observations after correction = sum of 50 observation + correct observation – incorrect observation 

= 4000 + 19 – 91

= 3928

∴ Corrected mean

= \( \cfrac{sum \,of \,observatiojns \,after \,correction }{Total \,number \,of \,observations}\)

= \(\frac{3928}{50}\)

= 78.56 

∴ The corrected mean is 78.56.