## Outliers In Data Sets

#### Aligned To Common Core Standard:

**High School Statistics** - HSS-ID.A.3

How to Spot Outliers in Data Sets -If we look at a setting outside the mathematics, we will find outliers everywhere. In mathematical terms, an outlier refers to an observation, that lies at an abnormal distance from the other values in a random sample taken from a population. In simpler terms, it can be defined as an observation point that lies away from the other observations. It is the examination of the unusual data points for that are removed from the mass of data. In order to spot an outlier, what you have to do is study and analyze the data thoroughly. Look for the unusual from the data. If you see any observation or number lying outside the range, data set or defined limit, know that it's an outlier. But in case of large amount of data, a peak into the data is not enough. Think about a data set having 500 columns and 10K+ rows, would you still be able to find out the outliers in just a peak? For cases such as these, there are a plenty of methods in statistics to find out these outliers. Some of these methods are complicated while others are not, however both are effective. These worksheets and lessons helps students learn to identify outliers in sets of data by using a variety of methods.

### Printable Worksheets And Lessons

- Finding Outliers Step-by-step Lesson- We look at the average when the extreme is removed.
- Guided Lesson - We start to grasp the reason that this skill can help you.
- Guided Lesson Explanation - You can quickly see that you can generalize from data that more representative of the average.
- Practice Worksheet - Some problems work off of the data table. Others come with their own data.
- Matching Worksheet - These don't seem like the same types of problems at first, but you should see it by number 3.

#### Homework Sheets

Let's see how much those outliers messed up our wonderful averages.

- Homework 1 - The following table displays the sales of different brands of televisions.
- Homework 2 - An outlier is a piece data that is drastically higher or lower than all the other data.
- Homework 3 - 35 students scored an average 75 out of 110 points on the English test. 5 students scored extremely high. When these 5 students were excluded, the average was reduced to 71 out of 110.

#### Practice Worksheets

Some really interesting scenarios can be found in these sheets.

- Practice 1 - 55 students scored an average of 85 out of 150 on the History test. 5 students scored extremely high points. When these 5 students were excluded the average was reduced to 80 out of 150. What is the mean of the 5 outliers?
- Practice 2 - If the score of the outlier is not included, what is the mean score?
- Practice 3 - Ms. Sonia has 75 students in her class. In a graded evaluation the students averaged 65%. Due to a calculation mistake, she thought the students had averaged 66%. The calculation mistake was that 5 students who scored low points were excluded.

#### Math Skill Quizzes

If your students do well on these, they should have no problem. 2 problems on each quiz are deemed "difficult", by national standards.

- Quiz 1 - 60 students scored an average of 65 out of 150 on the Painting test. 5 students scored extremely high points. When these 5 students were excluded the average was reduced to 60 out of 150. What is the mean of the 5 outliers?
- Quiz 2 - The following table displays the soft drink sales.
- Quiz 3 - If the score of the outlier is not included, what is the mean score?