Question

the graph shows a distribution of data. what is the standard deviation of the data? 0.5 1.5 2.0 2.5

Explanation:

Step1: Recall normal - distribution property

In a normal distribution, approximately 68% of the data lies within 1 standard - deviation of the mean. If the mean is at \(x = 2\), and we assume the data is normally distributed, 68% of the data lies between \(x=1.5\) and \(x = 2.5\).

Step2: Calculate standard deviation

The distance from the mean (\(\mu = 2\)) to either \(x = 1.5\) or \(x=2.5\) is \(|2 - 1.5|=|2.5 - 2| = 0.5\). Since this distance represents 1 standard - deviation (\(\sigma\)) in a normal distribution, the standard deviation \(\sigma=0.5\).

Answer:

0.5