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

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,
$σ^2=\frac{∑y_{i}^{2}}{38}−(\frac{∑y_i}{38})^2$
$=\frac{36756}{38}−(\frac{1178}{38})^2=−31^2$
$38σ^2=36756–36518=238$