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Supplemental Math: Study Aid1 chapters | 19 lessons

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Lesson Transcript

Instructor:
*Yolanda Williams*

Yolanda has taught college Psychology and Ethics, and has a doctorate of philosophy in counselor education and supervision.

Skewed distributions are asymmetrical and have data that clusters toward one end. In this lesson, learn about positively skewed distributions, negatively skewed distributions, and more.

Imagine that you were interested in studying the annual income of students one year after they have completed their Masters of Business Administration (MBA). You collect data from 400 graduates and find that their yearly income ranges from $20,000 to $150,000. This table summarizes the data that you have collected.

Let's say that you are also interested in examining the number of applications each graduate completed before they found their current job. Using data collected from the same 400 graduates, you find that the number of applications they completed ranges from 1 to 15. This table summarizes the data that you have collected.

You probably could not tell by looking at the tables, but the data you collected in both of the studies above is skewed.

A distribution is said to be **skewed** when the data points cluster more toward one side of the scale than the other, creating a curve that is not symmetrical. In other words, the right and the left side of the distribution are shaped differently from each other. There are two types of skewed distributions.

A distribution is **positively skewed** if the scores fall toward the lower side of the scale and there are very few higher scores. Positively skewed data is also referred to as skewed to the right because that is the direction of the 'long tail end' of the chart. Let's create a chart using the yearly income data that we collected from the MBA graduates.

You can see that most of the graduates reported annual income between $31,000 and $70,000. You can see that there are very few graduates that make more than $70,000. The yearly income for MBA graduates is positively skewed, and the 'long tail end' of the chart points to the right.

A distribution is **negatively skewed** if the scores fall toward the higher side of the scale and there are very few low scores. Let's take a look at the chart of the number of applications each graduate completed before they found their current job.

We can see that most of the graduates completed between 9 and 13 applications. Only 56 out of the 400 graduates completed less than 9 applications. The number of applications completed for MBA graduates is negatively skewed, and the 'long tail end' points to the left. Negatively skewed data is also referred to as 'skewed to the left' because that is the direction of the 'long tail end.'

You are probably somewhat familiar with the mean, median, and mode. The **mode** is the most frequently occurring score in a distribution. The **median** is the middle value that separates the top 50% of the distribution from the bottom 50%. The **mean** is the average found by adding all of the scores together and dividing the sum by the total number of scores.

The mean, median, and mode are measures of central tendency that are used to describe a data set. Here are a few key points to remember:

- In a positively skewed distribution, the mean is usually greater than the median because the few high scores tend to shift the mean to the right.
- In a negatively skewed distribution, the mean is usually less than the median because the few low scores tend to shift the mean to the left.
- In a positively skewed distribution, the mode is always less than the mean and median. This is because the mode is the point on the
*x*-axis corresponding to the highest point, and the highest point in a positively skewed distribution will always be on the lower side. - In a negatively skewed distribution, the mode is always greater than the mean and median, and the highest point in a negatively skewed distribution will always be on the right side.

There are some data that are naturally skewed. For example, age at retirement is negatively skewed since most people don't tend to retire until their 60s and very few people retire before then. The number of children in U.S. households is an example of data that is positively skewed; most U.S households have between zero and five children, and there are very few households with six or more children. Household income in the U.S. is also positively skewed.

A distribution is said to be **skewed** when the data points cluster more toward one side of the scale than the other. A distribution is **positively skewed**, or skewed to the right, if the scores fall toward the lower side of the scale and there are very few higher scores. A distribution is **negatively skewed**, or skewed to the left, if the scores fall toward the higher side of the scale and there are very few low scores. In positively skewed distributions, the **mean** is usually greater than the **median**, which is always greater than the **mode**. In negatively skewed distributions, the mean is usually less than the median, which is always less than the mode.

Once you are done with this lesson you should be able to:

- Explain how data can become skewed
- Recall the appearance of and identify positively and negatively skewed data
- Describe how the mean, median and mode can indicate if data is positively or negatively skewed

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Supplemental Math: Study Aid1 chapters | 19 lessons

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