### All about outliers

**Directions for teachers:**

Ask students to discuss the first set of questions with a partner, then read the online *Science News* article “Why do some people succeed and other fail? Outliers provide clues” before discussing the second set of questions as a class. A version of the article, “Look to the Outliers,” appears in the February 26, 2022 issue of *Science News. *

**Want to make it a virtual lesson?** Post the online *Science News *article to your virtual classroom. Discuss the article and questions with your class on your virtual platform.

**Outlining outliers**1. Draw a picture or diagram that describes the meaning of an outlier.

*Student answers will vary but may include a grouping of data with a point or two lying outside of the grouping. On a graph, outliers appear far away from other clustered points. On a distribution curve, outliers occur at the tail ends of the curve due to their low probability of occurrence. Students may use box plots or scatter diagrams if they have learned about them in the past.*

2. Describe what an outlier is in words. How would you tailor your definition to apply to math or science?

*An outlier exists outside of what is considered normal or average for a population. In math or science, outliers are anomalous data points within a dataset.*

3. Why do outliers occur? Name as many reasons as you can.

*Outliers can occur from sampling errors, data entry errors, measurement errors or other procedural mistakes. They can also occur from natural variation. *

4. What are some techniques used to identify outliers in math and science datasets?

*If the dataset is small, you might be able to detect outliers by in the data by eye. Otherwise, you would have to either use a graph or other data visualization or a statistical test to determine whether outliers exist. Common statistical tests include box plots, Z-score and inner quartile ranges. Scatter plots and distribution curves can also be useful ways of identifying outliers.*

5. In what ways can outliers impact data analysis? Should outliers always be removed from a dataset? Explain.

*Averages, standard deviations, correlations and related statistics are highly sensitive to outliers. Including outliers when analyzing data increases data variability and decreases statistical power. Excluding outliers decreases data variability and increases statistical power, possibly giving the false appearance of statistical significance. An outlier should be discarded if it was known to be the result of an erroneous measurement. But in most cases, outliers may provide important insights about individuals within the study population and so should not be discarded.*

**Positive deviance**

1. Explain the positive deviance approach that is described in the *Science News* article. How can positive deviance be useful for solving societal problems?

*The positive deviance approach is the process of looking at groups or individuals that qualify as outliers within a dataset to try to gain important insight into why they exist as outliers. Looking at the behaviors of outliers that led to positive outcomes may point to solutions for people or communities that are struggling.*

2. Choose an example of positive deviance from the article and explain it.

*Somali villages that have sustainable grazing are outliers because most of the region’s grazing lands have been destroyed by years of drought. Researchers investigated these outliers, or deviants, to determine how the villages maintained healthy vegetation and to see if the practices could be replicated elsewhere.*

3. Revisit your answer to question No. 5 in the previous set of questions. Would you change or modify your original answer after reading the article? Explain why or why not.

*Student answers will vary, but they should mention that not all outliers should be thrown away.*

4. Brainstorm your own example of positive deviance. What is a study that could be done in which investigating the outliers might lead to important insights or information?

*Student answers will vary. A study of teenagers’ time spent on social media over the course of a week could create an opportunity for positive deviance. If most teens spend a lot of time on social media, the outliers may be able to provide insights into alternative engagement opportunities for teens**. *