Question

The mean and standard deviation of 40 observations are 30 and 5 respectively. It was noticed that two of these observations 12 and 10 were wrongly recorded. If σ is the standard deviation of the data after omitting the two wrong observations from the data, then 38σ² is equal to ______.

Answer 1

Correct Answer: 238

The correct answer is 238
\(μ=\frac{∑x_i}{40}=30 ⇒∑x_i=1200\)
\(σ^2=\frac{∑x^{2}_{i}}{40}−(30)2=25 ⇒ ∑x_{i}^{2}=37000\)
After omitting two wrong observations
\(∑y_i=1200−12−10=1178\)
\(∑y_{i}^{2}=37000−144−100=36756\)
Then,
\(σ^2=\frac{∑y_{i}^{2}}{38}−(\frac{∑y_i}{38})^2\)
\(=\frac{36756}{38}−(\frac{1178}{38})^2=−31^2\)
\(38σ^2=36756–36518=238\)