Question

the graph shows the distribution of hand lengths, in centimeters, of the members of an orchestra. what is the variance of the data? 1 2 4 5

Explanation:

Step1: Recall the relationship between standard deviation and variance in a normal distribution

In a normal distribution, if we assume the distance from the mean to one of the marked points (say from the mean \( \mu = 19\) to \(x = 21\)) represents one - standard deviation (\(\sigma\)). Here, \(\sigma=2\) (since \(21 - 19=2\)).

Step2: Use the formula for variance

The formula for variance is \(\sigma^{2}\). Given \(\sigma = 2\), then \(\text{Variance}=\sigma^{2}\).
Substitute \(\sigma = 2\) into the formula: \(\text{Variance}=2^{2}\)

Answer:

\(4\)