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: Determine the standard deviation

In a normal distribution, the distance from the mean ($\mu = 4$) to the inflection point (e.g., $x = 4.5$) gives the standard deviation ($\sigma$). So, $\sigma=4.5 - 4=0.5$.

Step2: Calculate the variance

The formula for variance ($\sigma^{2}$) is $\sigma^{2}=(\sigma)^{2}$. Substituting $\sigma = 0.5$, we get $\sigma^{2}=(0.5)^{2}=0.25$.

Answer:

0.25