Question

In a group of 200 students, the mean and the standard deviation of scores were found to be 40 and 15, respectively. Later on it was found that the two scores 43 and 35 were misread as 34 and 53, respectively. The corrected mean of scores is:
1. 40.965
2. 39.035
3. 39.965
4. 40.035

Answer 1

Correct Answer - Option 3 : 39.965

Concept:

• Average/Mean: Mean of 'n' observations = \(\rm \overline x=\frac{\text{Sum of Observations}}{n}\).

• If some values are changed/added/removed, then Average_new = Average_old + (Average of the change), where the "Average of the change" is calculated for the final total number of objects.

 

Calculation:

Here, the final number of students is 200 (no change).

The change in the value is: (43 - 34) + (35 - 53) = 11 - 18 = -7.

Using Averagenew = Averageold + (Average of change), we have:

Averagenew = 40 + \(\left(\frac{-7}{200}\right)\)

= 40 - 0.035

= 39.965