Question

The graph shows the distribution of hand lengths, in centimeters, of the members of an orchestra.

A graph shows the horizontal axis numbered 14 to x. The vertical axis is unnumbered. The graph shows an upward trend from 14 to 19 then a downward trend from 19 to 24.
What is the variance of the data?

1
2
4
5

Answer 1

The 3rd option is correct.

Variance = 4

Explanation:

The graph for the question is missing, but after checking online, it was obtained, although, I'm skeptical of adding the image obtained in order not to violate the community guidelines and lead to deleted answers. So, I'll just describe the graph.

The graph is a bell shaped graph, with the central point at 19 and the rest of the distribution spreading limit from the centre with distributions ranging from 14 to x shown on the x-axis. The spread of the hand length on the x-axis from the center mean of 19, is in multiples of 2 cm.

The bell shaped graph corresponds to that of a normal distribution, the center of the curve being 19 indicates that this is the mean of the distribution and the spread of the distriburion from the mean (2 cm) indicates the standard deviation for the normal distribution.

And the relationship between standard deviation and the variance is given as

Standard deviation = √(variance)

2 = √(variance)

Variance = 2² = 4

Hope this Helps!!!