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 property of normal - distribution variance

For a normal distribution, if the inflection points are at $x = \mu\pm\sigma$, and we can estimate the standard - deviation $\sigma$ from the graph. The inflection points of a normal distribution curve are the points where the curve changes concavity. Here, assume the mean $\mu = 4$. The inflection points seem to be at $x = 3.5$ and $x = 4.5$.

Step2: Calculate the standard - deviation

Since $\mu-\sigma=3.5$ and $\mu = 4$, then $4-\sigma = 3.5$, so $\sigma=0.5$.

Step3: Calculate the variance

The variance $\sigma^{2}$ is related to the standard - deviation $\sigma$ by the formula $\sigma^{2}=\sigma\times\sigma$. Substituting $\sigma = 0.5$ into the formula, we get $\sigma^{2}=(0.5)\times(0.5)=0.25$.

Answer:

0.25