Question

For a sequence of 100 observations, the mean and standard deviation are 40 and 10 respectively. In calculating these measures, two observations were taken as 30 and 70 instead of 3 and 27 by mistake. Find the corrected mean and corrected standard deviation.

Answer 1

Here, n = 100: x̄ = 40; s = 10
Wrong observation: 30, 70
True observations : 3, 27

Mean:
x̄ = Σx / n
∴ 40 = Σx / 100
∴ 4000 = Σx

Corrected mean:
Corrected Σx = Σx – (Sum of wrong observation) + (Sum of true observation)
= 4000 – (30 + 70) + (3 + 27)
= 4000 – 100 + 30 = 3930
Corrected Mean = 3930 / 100 = 39.3