bimodal histogram?

Question

What do we mean when we say that a histogram is skewed to the left? To the right? What is a bimodal histogram? Discuss the following statement: “A bimodal histogram usually results if we draw a sample from two populations at once.” Suppose you took a sample of weights of college football players and with this sample you included the weights of cheerleaders. Do you think a histogram made from the combined weights would be bimodal? Explain.

Answer 1

To add to Jon's answer, the reason we say "skewed left" or "skewed right" is because of the effect of outliers.

For example, take a look at this distribution of scores:

14 15 15 16 16 16 17 17 17 17 18 18 18 19 19 20

This is a symmetrical distribution of scores where the median is 17 and the mean is (14 + ... + 20)/16 = 272/16 = 17.

Now, let's change a single score:

14 15 15 16 16 16 17 17 17 17 18 18 18 19 19 52

The median of these 16 scores is still 17, but the mean is now (14 + ... + 52)/16 = 304/16 = 19. That is, this large outlier of 52 on the right side of the distribution skewed the mean toward the right.

Similarly, if we changed the original distribution to this:

6 15 15 16 16 16 17 17 17 17 18 18 18 19 19 20

The median is still 17, but the mean is now (6 + ... + 20)/16 = 264/16 = 16.5. This time, the mean was skewed to the left because of that outlier of 6 on the left side of the distribution.

Answer 2

When a histogram is skewed to the left, the median is greater than the mean.

When a histogram is skewed to the right, the median is less than the mean.

A bimodal histogram has two data peaks.

A histogram of cheerleader and football player weights would be bimodal because the football players weights are greater than the cheerleaders, so the distributions of their weights would be offset from one another.