For a group of 200 candidates, the mean and standard deviations of scores were found to be 40 and 15 respectively. Later on it was discovered that the score of 43 was misread as 34. Find the correct mean and standard deviation.

Question

Philoid · Accepted Answer

Given that number of observations (n) = 200

Incorrect Mean (x̅ ) = 40

and Incorrect Standard deviation, (σ) = 15

We know that,

…(i)

∴ Incorrect sum of observations = 8000

Finding correct sum of observations, 43 was misread as 34

So, Correct sum of observations = Incorrect Sum – 34 + 43

= 8000 – 34 + 43

= 8009

Hence,

= 40.045

Now, Incorrect Standard Deviation (σ)

Squaring both the sides, we get

Since, 43 was misread as 34

So,

= 365000 – 1156 + 1849

= 125000 + 693

= 365693

Now,

Correct Standard Deviation

= 14.995

Hence, Correct Mean = 40.045

and Correct Standard Deviation = 14.995