Question

The mean of 11 observations is 28. It was found that one observation 34 was misread as 23. Find the mean if:

1. this observation is excluded. 
2. correct observation is included.

Answer 1

Given:

Mean of 11 observations = 28.

One observation 34 was misread as 23.

Total (recorded) sum of 11 observations = 11 × 28 = 308.

a. If the (misread) observation is excluded:

Sum of remaining 10 observations

= 308 – 23

= 285

New mean

= 285 ÷ 10 

= 28.5

b. If the correct observation (34) is included (i.e., replace 23 by 34):

Corrected total sum

= 308 – 23 + 34

= 319

New mean

= 319 ÷ 11

= 29