Unmasking Outliers: Mastering Box and Whisker Plots

Algebra 2 Grades High School 4:23 Video
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Lesson Description

Learn to identify outliers in data sets using box and whisker plots and the 1.5 IQR rule. This lesson covers constructing box plots and interpreting their components.

Video Resource

Outliers - Box and Whisker Plot (1.5 IQR)

Mario's Math Tutoring

Duration: 4:23
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Key Concepts

  • Box and Whisker Plots
  • Interquartile Range (IQR)
  • Outliers (1.5 IQR Rule)

Learning Objectives

  • Construct a box and whisker plot from a given data set.
  • Calculate the interquartile range (IQR) of a data set.
  • Identify outliers using the 1.5 IQR rule.

Educator Instructions

  • Introduction (5 mins)
    Begin by defining what an outlier is and why it's important to identify them in data analysis. Briefly introduce box and whisker plots as a tool for outlier detection. (See Video 0:06)
  • Constructing Box and Whisker Plots (15 mins)
    Guide students through the process of creating a box and whisker plot. This includes finding the median, lower quartile (Q1), upper quartile (Q3), minimum, and maximum values. Explain how to handle data sets with an even number of values when finding the median and quartiles. (See Video 0:28 - 1:57)
  • Calculating the IQR (5 mins)
    Explain how to calculate the interquartile range (IQR) by subtracting the lower quartile (Q1) from the upper quartile (Q3). (See Video 2:44)
  • Identifying Outliers Using the 1.5 IQR Rule (10 mins)
    Introduce the 1.5 IQR rule for identifying outliers. Explain how to calculate the upper and lower bounds (Q1 - 1.5 * IQR and Q3 + 1.5 * IQR) and how any data points falling outside these bounds are considered outliers. (See Video 3:08)
  • Graphing Box and Whisker Plots (10 mins)
    Demonstrate how to graph the box and whisker plot on a number line, including plotting the median, quartiles, minimum, and maximum values. Explain how to represent outliers on the plot. (See Video 1:57-2:33)

Interactive Exercises

  • Data Set Analysis
    Provide students with several data sets and have them construct box and whisker plots for each. They should then calculate the IQR and identify any outliers using the 1.5 IQR rule.
  • Real-World Data
    Have students find real-world data sets (e.g., sports statistics, weather data) and analyze them for outliers. Discuss potential reasons for the outliers.

Discussion Questions

  • Why is it important to identify outliers in a data set?
  • How does the IQR help us understand the spread of data?
  • Can a data set have no outliers? Explain.
  • How might outliers affect the mean and median of a data set?

Skills Developed

  • Data Analysis
  • Statistical Reasoning
  • Problem-Solving
  • Visual Representation of Data

Multiple Choice Questions

Question 1:

What is an outlier?

Correct Answer: A data point that is significantly different from other data points in the set.

Question 2:

Which of the following is NOT needed to create a box and whisker plot?

Correct Answer: Mean

Question 3:

The interquartile range (IQR) is calculated by:

Correct Answer: Subtracting the lower quartile from the upper quartile.

Question 4:

The 1.5 IQR rule identifies outliers as data points that are:

Correct Answer: More than 1.5 times the IQR above the upper quartile or below the lower quartile.

Question 5:

What does the box in a box and whisker plot represent?

Correct Answer: The interquartile range (IQR).

Question 6:

Which of the following best describes the 'whiskers' in a box and whisker plot?

Correct Answer: They extend to the maximum and minimum values within 1.5 IQR of the quartiles.

Question 7:

If the lower quartile (Q1) is 20 and the upper quartile (Q3) is 50, what is the IQR?

Correct Answer: 30

Question 8:

Using the information from the previous question (Q1=20, Q3=50), what is the lower bound for outlier detection using the 1.5 IQR rule?

Correct Answer: -25

Question 9:

Using the information from the previous questions (Q1=20, Q3=50), what is the upper bound for outlier detection using the 1.5 IQR rule?

Correct Answer: 95

Question 10:

Which of the following is most affected by outliers?

Correct Answer: Range

Fill in the Blank Questions

Question 1:

A data point that is significantly different from other data points is called an ________.

Correct Answer: outlier

Question 2:

The middle value of a data set is called the ________.

Correct Answer: median

Question 3:

The range between the lower and upper quartiles is called the ________ ________.

Correct Answer: interquartile range

Question 4:

The 1.5 IQR rule uses 1.5 times the ________ ________ to determine outlier boundaries.

Correct Answer: interquartile range

Question 5:

The ________ quartile represents the median of the lower half of the data.

Correct Answer: lower

Question 6:

The ________ quartile represents the median of the upper half of the data.

Correct Answer: upper

Question 7:

The lines extending from the box in a box and whisker plot are called ________.

Correct Answer: whiskers

Question 8:

To find the upper bound for outliers, you add 1.5 times the IQR to the ________ quartile.

Correct Answer: upper

Question 9:

To find the lower bound for outliers, you subtract 1.5 times the IQR from the ________ quartile.

Correct Answer: lower

Question 10:

Outliers are represented individually as points beyond the ________ on a box and whisker plot.

Correct Answer: whiskers

Educational Standards

A2.D.1.1:Calculate measures of center and spread (i.e., mean, median, mode, range, interquartile range, standard deviation). Use these quantities to draw conclusions about the data. A2.D.1.2:Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of outliers.

Teaching Materials

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