Compute the mean and variance of the following data set: (50.1, 50.0, 49.8, 50.2, 49.9)

Concept:

The mean of a data set is the sum of all observations divided by the number of observations.

The variance is the average of the squared differences from the mean.

Calculation:

Given Data: 50.1, 50.0, 49.8, 50.2, 49.9

Step 1: Calculate the mean

\(\text{Mean} = \frac{50.1 + 50.0 + 49.8 + 50.2 + 49.9}{5} = \frac{250.0}{5} = 50.0\)

Step 2: Calculate the variance

Variance = \(\frac{(50.1 - 50)^2 + (50.0 - 50)^2 + (49.8 - 50)^2 + (50.2 - 50)^2 + (49.9 - 50)^2}{5}\)

\(=\frac{(0.1)^2 + (0)^2 + (-0.2)^2 + (0.2)^2 + (-0.1)^2}{5} = \frac{0.01 + 0 + 0.04 + 0.04 + 0.01}{5} = \frac{0.10}{5} = 0.02\)

Answer:

 Mean = 50.0, Variance = 0.02

Correct Option: 2) mean = 50.0, variance = 0.02