Question

The mean and sample standard deviation of the dataset consisting of 9 observations is 14 and 10 respectively. Later it is noted that one observation 11 is wrongly noted as 6. What is the mean of the original dataset? (Correct to 2 decimal place accuracy

Answer 1

Given, number of observations n=20

Incorrect mean =10

Incorrect standard deviation =2

xˉ=n1i=1∑20xi

10=201i=1∑20xi

⇒i=1∑20xi=200

So, the  incorrect sum of observations =200

Correct sum of observation =200−8=192

⇒ Correct mean =19Correctsum=19192=10.1

Standard deviation σ=n1i=1∑nxi2−n21(i=1∑nxi)2=n1