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 variance and standard deviation in a normal distribution

In a normal distribution, the variance is the square of the standard deviation. From the graph (assuming it's a normal - like distribution where the spread can be estimated visually), if we assume the standard deviation \(s = 0.5\) (a common visual - based estimate for such a bell - shaped curve in basic problems).

Step2: Calculate the variance

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

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Answer:

\(0.25\) (the second option)