Question

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

Explanation:

1. Recall the property of a normal - distribution graph:

• In a normal - distribution, if the graph is symmetric about the mean \(\mu\), and we assume that the points at one - standard deviation (\(\sigma\)) away from the mean are clearly marked. Here, if the mean \(\mu = 4\), and one of the points at one - standard deviation away from the mean is \(x = 4.5\) (or \(x = 3.5\)). Then the standard deviation \(\sigma=4.5 - 4=0.5\) (or \(4 - 3.5 = 0.5\)).

1. Use the formula for variance:

• The formula for the variance \(\sigma^{2}\) of a data - set is related to the standard deviation \(\sigma\) by \(\sigma^{2}=\sigma\times\sigma\).
• Since \(\sigma = 0.5\), then \(\sigma^{2}=(0.5)\times(0.5)=0.25\).

Answer:

0.25