Summary of Five Number Summary in Boxplots and Data Sets

Monitoring Your Readiness

To effectively plan and use your time wisely, it helps to think about what you know and do not know. For each of the following, rate how confident you are that you can successfully do that skill. Use the following descriptions to rate yourself:

5—I am extremely confident I can do this task.

4—I am somewhat confident I can do this task.

3—I am not sure how confident I am.

2—I am not very confident I can do this task.

1—I am definitely not confident I can do this task.

Skills Needed for Five Number Summary in Boxplots and Data Sets: Forming Connections

Skill or Concept: I can . . . Questions to check your understanding Rating from 1 to 5
Identify the features of a boxplot. 1, 7
Interpret the features of a boxplot. 2-4
Identify outliers in a data set. 5, 6, 8, 9
Relate a boxplot of a quantitative variable to its distribution. 10-12

Now use the ratings to get ready for your next in-class activity. If your rating is a 3 or below, you should get help with the material before class. Remember, your instructor is going to assume that you are confident with the material and will not take class time to answer questions about it.

Ways to get help:

  • See your instructor before class for help.
  • Ask your instructor for on-campus resources.
  • Set up a study group with classmates so you can help each other.
  • Work with a tutor.

Essential Concepts

  • A boxplot captures only the median of the data set, not the mean, as a measure of center. It provides a quick glance (or summary) of the data to make comparisons based on the median, skew, outliers, and percentiles.
  • The collection of the minimum, first quartile, median, third quartile, and maximum form the five-number summary of the variable.
  • There are several good methods to use for determining an observation to be an outlier in the distribution. The IQR method commonly uses a distance 1.5 times IQR from Q1 or Q3.

Study Tips: Evidence-based strategies for learning

  • Retrieval practices are helpful for remembering new terms and definitions.
    • Add the terms in the glossary along with their definitions and abbreviations to your set of flashcards. Remember to quiz yourself with your flashcard set for a few minutes every few days to prepare for high-stakes tests like the final exam.
    • Make up quiz questions for how to find the five number summary and the IQR of a data set. Write out solutions to these questions and check them for accuracy in the text.
  • Use mnemonics and sketches to help remember the features of a boxplot.
    • To provide the five number summary, remember MQMQM (minimum, Q1, median, Q3, maximum).
    • Reproduce the generic diagram of a boxplot at the top of the What to Know page from memory and check it to see if you accurately represented all the characteristics and their locations correctly.
    • Handwrite, without looking at the text or your notes, the formulas to calculate Q1, Q3, and IQR.
  • Together with others in your study group (or alone by taking a video on your phone) pretend that you are tutoring a student through the Forming Connections piece by explaining the answers to each of the questions. Critique each other’s explanations (or compare your video explanation to the correct answers) to refine your understanding of how to use boxplots to compare multiple distributions or to draw inferences.

Foundational Knowledge

Key Equations

  • Interquartile range (IQR)

Q3–Q1

  • Upper outlier

Q3 + 1.5 × (IQR), remember to multiply 1.5 by IQR first, then add to Q3

  • Lower outlier

Q1 – 1.5 × (IQR), remember to multiply 1.5 by IQR first, then subtract from Q1

Glossary

first quartile
the value below which one quarter of the data lies, also equal to the 25th percentile. Sometimes denoted Q1.
five-number summary
the collection of the minimum, first quartile, median, third quartile, and maximum of the variable.
interquartile range
the quantity Q3–Q1. Sometimes denoted IQR.
lower outlier
an observation that is less than Q1 – 1.5 × (IQR).
third quartile
the value below which three quarters of the data lay, also equal to the 75th percentile. Sometimes denoted as Q3.
upper outlier
an observation that is greater than Q3 + 1.5 × (IQR).

 

My Skills Checklist:

  • I can provide visual summaries of quantitative variables using boxplots.
  • I can compare the distributions of multiple populations using boxplots.
  • I can compare and draw inferences from boxplots.

Check mark list on clipboard

 Topic Complete – now test your understanding in the Self-Check.