Question

The Standard Deviation of 2, 4, 6, 8, 10 is

• A. \( \sqrt{6} \)
• B. \( 2\sqrt{3} \)
• C. \( 2\sqrt{2} \)
• D. \( 3\sqrt{2} \)

Hint:

To calculate the standard deviation, first find the mean, then calculate the variance by averaging the squared differences from the mean, and finally take the square root.

Answer 1

The Correct Option is C

The formula for the standard deviation \( \sigma \) of a data set \( x_1, x_2, \dots, x_n \) is: \[ \sigma = \sqrt{\frac{1}{n} \sum_{i=1}^{n} (x_i - \mu)^2}, \] where \( \mu \) is the mean of the data set. First, find the mean: \[ \mu = \frac{2 + 4 + 6 + 8 + 10}{5} = 6. \] Now, calculate the variance: \[ \text{Variance} = \frac{1}{5} \left( (2 - 6)^2 + (4 - 6)^2 + (6 - 6)^2 + (8 - 6)^2 + (10 - 6)^2 \right) = \frac{1}{5} (16 + 4 + 0 + 4 + 16) = \frac{40}{5} = 8. \] The standard deviation is the square root of the variance: \[ \sigma = \sqrt{8} = 2\sqrt{2}. \]