The mean and standard deviation of 18 observations are found to be 7 and 4 respectively. On rechecking it was found that an observation 12 was misread as 21. Calculate the correct mean and standard deviation.
Given that number of observations (n) = 18
Incorrect Mean (x̅ ) = 7
and Incorrect Standard deviation, (σ) = 4
We know that,
…(i)
∴ Incorrect sum of observations = 126
Finding correct sum of observations, 12 was misread as 21
So, Correct sum of observations = Incorrect Sum – 21 + 12
= 126 – 21 + 12
= 117
Hence,
= 6.5
Now, Incorrect Standard Deviation (σ)
Squaring both the sides, we get
Since, 12 was misread as 21
So,
= 1170 – 441 + 144
= 873
Now,
Correct Standard Deviation
= 2.5
Hence, Correct Mean = 6.5
and Correct Standard Deviation = 2.5