The shape of a distribution helps explain how its mean, median, and mode relate to one another. In this lesson, you will learn to recognize symmetric and skewed distributions and understand how skewness affects measures of center.
A distribution is symmetric when a vertical line can divide its shape into two sides that are mirror images. For a perfectly symmetric distribution, the mean and median are equal. They are often also equal to the mode when the distribution has one mode.
All flashcards
What is a symmetric distribution?
A distribution whose shape on one side of a vertical line is a mirror image of its shape on the other side.
How is the direction of skew named?
By the direction of the distribution's longer tail. A tail toward smaller values indicates left skew; a tail toward larger values indicates right skew.
What is the common relationship between mean and median in a left-skewed distribution?
The mean is often less than the median because low values in the tail can pull the mean downward.
Why is the median less sensitive to outliers than the mean?
The median depends on the middle position in the ordered data, rather than on the size of every value.
What do unimodal and bimodal mean?
A unimodal distribution has one mode; a bimodal distribution has two modes.
Quiz questions
In a perfectly symmetric distribution, what relationship holds between the mean and median?Answer: They are equal.
A distribution has a longer tail toward larger values. What is the direction of its skew?Answer: It is skewed to the right.
What does the mode of a data set describe?Answer: The value that occurs most frequently.
A symmetric distribution has two modes. What is possible about those modes?Answer: They need not equal the mean and median.
Why are mean-and-median patterns associated with skewness not guaranteed for every data set?Answer: Discrete data and unusual distributions can produce exceptions.
Based on Introductory Statistics 2e by Barbara Illowsky, Susan Dean (OpenStax), licensed CC BY 4.0. Adapted into a summary, flashcards and quizzes.