Question

the mean of 40 observation was 160 it was detected on rechecking that the value 165 was wrongly copied as 125 for computation of mean find the correct mean

Answer 1

Mean of 40 observations = 160
Hence,
Total sum of 40 observations = 160 * 40

On performing simple multiplication,

Total sum of 40 observations = 6400

Now,

Correct sum of 40 observations = 6400 - ( Incorrect Observation ) + ( Correct Observation )

Putting the values in the given formula,

Correct sum of 40 observations = 6400 - ( 165 ) + ( 125 )

Removing brackets,

Correct sum of 40 observations = 6400 - 165 + 125

Performing addition first as per BODMAS,

Correct sum of 40 observations = 6525 - 165

Performing substraction as per BODMAS,

Correct sum of 40 observations = 6360

Now,

The correct mean of 40 observations = 6360 / 40

Performing simple division,

The correct mean of 40 observations = 159