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The Effects of Outliers on Centers of Measure

The Effects of Outliers on Centers of Measure

Author: Kate Sidlo
Description:

By the end of this tutorial a student will be able to ...

  1. Calculate the IQR from a box-and-whisker plot
  2. Define outlier using IQR
  3. Find if a value is an outlier for a set using the IQR definition
  4. Know how outliers affect the measures of center (mean, median, and mode)

... by successfully completing the quiz in the tutorial, discussing real-world examples in a short writing assignment, and through a mini-activity including a review of box-and-whisker plots and measure of center.

This tutorial walks students through IQR and outliers in a short video then helps students explore outliers with measures of centers through a series of activities.  Students check their understanding through a quiz.

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Tutorial

How to Complete the Tutorial

  1. Watch the video below or click through the slides and take notes to help you in the following steps.
  2. Read and complete Task 1.
    (You will need you own piece of paper or word processing - Word/Google Docs etc.)
  3. Read and complete Task 2. 
    (You will need your journal entry and possibly a calculator)
  4. Complete Task 3 (the quiz on the side), if you need additional help, check the vocabulary box and the additional resources at the bottom of the page)

Definition of Outliers & IQR

Definition of Outliers & IQR [Slides Only]

Full Screen

TASK 1: Real-World Outliers | Reading & Reflection

Full Screen

TASK 2 | Outlier Effect on Measures of Center | Mini-Activity

On the same sheet of paper as your journal create another title "Task 2: Mini-Activity".

Next copy a picture of the following dot plot on your paper.  This dot plot shows the ages of people at a local movie theater on Saturday afternoon.

 

 

 

 

Complete the following steps.  Show your work for full credit.

  1. Find the mean, median, and mode for the data above (called data set 1)
  2. Find the quartiles for the data.
  3. Create a box and whisker plot for the data
  4. Calculate the IQR for the data and discuss if any outliers are present.  Explain your answer using the formal definition of an outlier.

     
  5. Write the data set in order from least to greatest WITHOUT the outliers (now called data set 2)
  6. Find the mean, median, and mode for data set 2
  7. Compare the mean from data set 1 to data set 2.  Make note of any changes and what may account for them.
  8. Compare the median from data set 1 to data set 2.  Make note of any changes and what may account for them.
  9. Compare the modes from data set 1 to data set 2.  Make note of any changes and what may account for them.

     
  10. Write a summary about how you think outliers may or may not effect data sets.  This must be at least three complete sentences.
  11. Write one to two complete sentences about why you think Mrs. Sidlo chose to use a picture of someone stretching pizza dough for the tutorial.

TASK 3 | Assessment of Notes

Take the four question quiz on the right side of the page near the top.  If you don't feel ready review the vocabulary and/or the additional resources at the bottom of the page.

VOCABULARY:

BOX-AND-WHISKER PLOT: A data display that shows the median, quartiles, maximum, and minimum terms along a number line.

INTER QUARTILE RANGE (IQR): The difference (range) of the upper quartile and lower quartile

MAXIMUM: The largest term in a data set

MEAN: The "average" of a data set found by dividing the sum of the terms by the number of terms

MEDIAN:  The middle term in a data set when the terms are in order from least to greatest, if there are two terms, the median is the mean of the two digits

MINIMUM: The smallest term in a data set

MODE: The most common term or terms in a data set

OUTLIER: A term that lies far outside the range and trend of other data points in a set; formally defined as less than Q1 - 1.5(IQR) or more than Q3 + 1.5(IQR)

QUARTILE: The median of the upper half and lower half of a data set (not including the median)

ADDITIONAL RESOURCES

Purple Math Article | Box-and-Whisker Plots: IQR & Outliers

WikiHow Article | How to Calculate Outliers: 7 Steps (covers quartiles, outliers, & IQR)

Youtube Video | MySecretMathTutor: How to Find Outliers (covers quartiles, outliers, & IQR)