Learn on PengiBig Ideas Math, Course 1Chapter 10: Data Displays

Lesson 4: Box-and-Whisker Plots

In this Grade 6 lesson from Big Ideas Math, Course 1, Chapter 10, students learn how to construct and interpret box-and-whisker plots using the five-number summary, which includes the least value, greatest value, median, first quartile, and third quartile. Students practice ordering data sets, identifying quartiles, and drawing plots on a number line to display the variability of real-world data. The lesson also covers comparing two box-and-whisker plots to analyze and contrast data distributions.

Section 1

Introduction to Box-and-Whisker Plots

Property

A box-and-whisker plot displays data distribution using five key values: minimum, first quartile (Q1Q_1), median (Q2Q_2), third quartile (Q3Q_3), and maximum. The box represents the interquartile range (IQR) where IQR=Q3−Q1IQR = Q_3 - Q_1, and the whiskers extend to the minimum and maximum values.

Examples

Section 2

Constructing a Box Plot

Property

Box plots provide a visual image of the 5 number summary. To create a box plot:

  1. Draw a number line that covers the range of the data.
  2. Draw a rectangle (the box) from Q1 to Q3.
  3. Draw a vertical line segment inside the box at the median (Q2).
  4. Draw horizontal line segments (the whiskers) from the box to the Minimum and Maximum values.

Examples

  • For a 5 number summary of {10, 15, 19, 24, 30}, a box plot would have a box from 15 to 24, a line at 19, a left whisker to 10, and a right whisker to 30.
  • If a box plot has a very long right whisker and the median line is to the left of the box's center, it suggests the data is skewed right, with some high values stretching the data out.
  • Comparing two box plots, one with an IQR of 5 and another with an IQR of 20 shows that the middle 50% of the data in the second plot is much more spread out.

Explanation

A box plot turns the 5 Number Summary into a simple picture. The 'box' shows the spread of the middle 50% of data (IQR), and the 'whiskers' show the spread of the lowest and highest 25%. A wider section means the data in that part is more spread out.

Lesson overview

Expand to review the lesson summary and core properties.

Expand

Section 1

Introduction to Box-and-Whisker Plots

Property

A box-and-whisker plot displays data distribution using five key values: minimum, first quartile (Q1Q_1), median (Q2Q_2), third quartile (Q3Q_3), and maximum. The box represents the interquartile range (IQR) where IQR=Q3−Q1IQR = Q_3 - Q_1, and the whiskers extend to the minimum and maximum values.

Examples

Section 2

Constructing a Box Plot

Property

Box plots provide a visual image of the 5 number summary. To create a box plot:

  1. Draw a number line that covers the range of the data.
  2. Draw a rectangle (the box) from Q1 to Q3.
  3. Draw a vertical line segment inside the box at the median (Q2).
  4. Draw horizontal line segments (the whiskers) from the box to the Minimum and Maximum values.

Examples

  • For a 5 number summary of {10, 15, 19, 24, 30}, a box plot would have a box from 15 to 24, a line at 19, a left whisker to 10, and a right whisker to 30.
  • If a box plot has a very long right whisker and the median line is to the left of the box's center, it suggests the data is skewed right, with some high values stretching the data out.
  • Comparing two box plots, one with an IQR of 5 and another with an IQR of 20 shows that the middle 50% of the data in the second plot is much more spread out.

Explanation

A box plot turns the 5 Number Summary into a simple picture. The 'box' shows the spread of the middle 50% of data (IQR), and the 'whiskers' show the spread of the lowest and highest 25%. A wider section means the data in that part is more spread out.