Question

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

Explanation:

Step1: Recall variance property of normal - like distribution

For a normal - like distribution (the given distribution of hand - lengths looks approximately normal), if we assume that the empirical rule for normal distributions applies. In a normal distribution, about 95% of the data lies within 2 standard deviations of the mean. If we estimate the range of the data that contains about 95% of the values. Here, if we assume the mean is around 19. The range from about 17 to 21 might contain about 95% of the data. So, the distance from the mean to the end - point of this range is 2, which is approximately 2 standard deviations ($2\sigma$).

Step2: Calculate standard deviation

If $2\sigma = 2$, then $\sigma=1$.

Step3: Calculate variance

The variance $\sigma^{2}$. Since $\sigma = 1$, then $\sigma^{2}=1$.

Answer:

1