Question

the graph shows a distribution of data. what is the variance of the data? 0.0625 0.25 0.5 1.5

Explanation:

Step1: Recall the relationship between standard deviation and variance

For a normal distribution, if we assume the distance from the mean ($\mu = 4$) to a point (say $x = 4.5$) which is one - standard deviation ($\sigma$) away. Here, $\sigma=0.5$.

Step2: Use the formula for variance

The formula for variance is $\sigma^{2}$. Substitute $\sigma = 0.5$ into the formula. Then $\sigma^{2}=(0.5)^{2}$.
$$(0.5)^{2}=0.25$$

Answer:

0.25