Frequency Distribution Question

Question

A group of physically fit adults are taking part in a race. If you were to take all their times and plot them on a frequency graph, what skew do you think it would be?

Answer 1

In all practicality, there is a minimum number for running a certain distance, The super athlete, Olympic-type runner, would get a score that we could call a minimum time for the distance. All runners that are fit would be close the that but not less than it. So I would say the frequency distribution would look something like this:

This type of skew, with the tail going off to the right, is called Right Skew. That would be what I would think the results would be.

Answer 2

Hi Dee-Dee,

Let's talk about skewness before we dive into your question; there are three kinds of distributions/skews:

Left:

Also known as a negative skew, is named in the direction of the distributions tail. Here, the mean is less than the mode.

Normal:

This is the bell curve, where the distribution is symmetrical on both sides of the center. Here, the mean equals the mode.

Right:

Also known as a positive skew, is named in the direction of the distributions tail. Here, the mean is greater than the mode.

Now let's turn our attention to the race of physically fit adults.

Given the information these adults are physically fit, their race times would be faster than the average person. This means that it would be expected that a majority of the racers times would cluster on the lower end of the distribution tailing off with the slower times to the right. This would push the mean to be greater than the mode.

A right-tail and mean>mode fits the definition of a Right Skew (aka a Positive Skew).

Thus, it can be assumed that the race may result in a Right/Positive Skew.