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 the property of normal distribution

In a normal distribution, the distance from the mean to the inflection point is equal to the standard deviation.

Step2: Identify the mean and inflection point

The mean of the distribution is at \(x = 2\). The inflection points are at \(x=1.5\) and \(x = 2.5\).

Step3: Calculate the standard deviation

The distance from the mean \(x = 2\) to the inflection point \(x=1.5\) (or \(x = 2.5\)) is \(|2 - 1.5|=0.5\) (or \(|2.5 - 2| = 0.5\)).

Answer:

\(0.5\)