Question

The variance of the data \( 2, 4, 6, 8, 10 \) is:

• A. 8
• B. 7
• C. 6
• D. None of these

Hint:

Variance measures how far data points are from the mean. It is calculated as the average of the squared differences from the mean.

Answer 1

The Correct Option is A

Step 1: To calculate the variance, we use the formula: \[ {Variance} = \frac{1}{n} \sum_{i=1}^{n} (x_i - \mu)^2, \] where \( \mu \) is the mean of the data and \( n \) is the number of data points. 
Step 2: Calculate the mean: \[ \mu = \frac{2 + 4 + 6 + 8 + 10}{5} = \frac{30}{5} = 6. \] 
Step 3: Compute the squared differences from the mean: \[ (2 - 6)^2 = 16, \quad (4 - 6)^2 = 4, \quad (6 - 6)^2 = 0, \quad (8 - 6)^2 = 4, \quad (10 - 6)^2 = 16. \] 
Step 4: Compute the variance: \[ {Variance} = \frac{16 + 4 + 0 + 4 + 16}{5} = \frac{40}{5} = 8. \]