Question

The standard deviation of the data 6, 7, 8, 9, 10 is

• A. \(\sqrt2\)
• B. \(\sqrt{10}\)
• C. 2
• D. 10

Answer 1

The Correct Option is A

We need to find the standard deviation of the data: 6, 7, 8, 9, 10.

Step 1: Calculate the mean (\(\mu\)):

\(\mu = \frac{6+7+8+9+10}{5} = \frac{40}{5} = 8\)

Step 2: Calculate the variance (\(\sigma^2\)):

\(\sigma^2 = \frac{\sum (x_i - \mu)^2}{N}\)

\(\sigma^2 = \frac{(6-8)^2 + (7-8)^2 + (8-8)^2 + (9-8)^2 + (10-8)^2}{5}\)

\(\sigma^2 = \frac{(-2)^2 + (-1)^2 + (0)^2 + (1)^2 + (2)^2}{5}\)

\(\sigma^2 = \frac{4 + 1 + 0 + 1 + 4}{5} = \frac{10}{5} = 2\)

Step 3: Calculate the standard deviation (\(\sigma\)):

\(\sigma = \sqrt{\sigma^2}\)

\(\sigma = \sqrt{2}\)

Therefore, the standard deviation is \(\sqrt{2}\).

The correct option is (A) \(\sqrt{2}\).