Calculate the variance for the following data:

2, 5, 6, 8, 9

Correct option is C

​Given:

Data set: 2, 5, 6, 8, 9

Formula Used:

​$$\text{Variance} (\sigma^2) = \frac{1}{n} \sum (x_i - \bar{x})^2$$​​

where $$\bar{x}$$​ is the mean of the data and n is the number of data points.

Solution:
$$\bar{x} = \frac{2 + 5 + 6 + 8 + 9}{5} = \frac{30}{5} = 6$$​

Squared deviations from the mean

​$$(2 - 6)^2 = 16,\quad (5 - 6)^2 = 1,\quad (6 - 6)^2 = 0 \quad, (8 - 6)^2 = 4,\quad (9 - 6)^2 = 9$$​​

Sum of squared deviations

16 + 1 + 0 + 4 + 9 = 30

​$$\text{Variance} = \frac{30}{5} = 6$$​​