Mathematics
Grade 8
15 min
Interpret box-and-whisker plots
Interpret box-and-whisker plots
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1
Introduction & Learning Objectives
Learning Objectives
Identify the five-number summary (minimum, Q1, median, Q3, maximum) from a box-and-whisker plot.
Calculate the Interquartile Range (IQR) from a box-and-whisker plot.
Describe the spread and central tendency of a dataset represented by a box-and-whisker plot.
Compare two or more datasets using their respective box-and-whisker plots.
Explain what each section of a box-and-whisker plot represents in terms of data percentage.
Draw conclusions about data distribution, such as skewness or symmetry, from a box-and-whisker plot.
Ever wondered how to quickly see the spread of test scores in your class or compare the heights of two different plant species? 📊 Box-and-whisker plots are powerful tools for just that!
In this lesson, you'll learn how to read and...
2
Key Concepts & Vocabulary
TermDefinitionExample
Box-and-Whisker PlotA standardized way of displaying the distribution of data based on a five-number summary: minimum, first quartile (Q1), median (Q2), third quartile (Q3), and maximum.A plot showing student test scores, where the box represents the middle 50% of scores and the whiskers show the full range.
Five-Number SummaryThe five key values that describe the distribution of a dataset: minimum value, first quartile (Q1), median (Q2), third quartile (Q3), and maximum value.For the data set {10, 12, 15, 18, 20, 22, 25}, the five-number summary might be 10 (min), 12 (Q1), 18 (median), 22 (Q3), 25 (max).
Median (Q2)The middle value of a dataset when it is ordered from least to greatest. It divides the data into two equal halves.In the dataset {5, 7, 9, 11, 13}, the...
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Core Formulas
Understanding Data Distribution by Quartiles
Each of the four sections created by the box-and-whisker plot (from min to Q1, Q1 to median, median to Q3, and Q3 to max) represents approximately 25% of the data points.
This rule helps you understand how data is distributed. A longer section indicates a wider spread of data points within that 25%, while a shorter section indicates data points are clustered more closely.
Calculating the Interquartile Range (IQR)
$$IQR = Q_3 - Q_1$$
Use this formula to find the spread of the middle 50% of your data. A smaller IQR means the middle data points are more consistent or clustered, while a larger IQR means they are more spread out.
Identifying the Five-Number Summary
The box-and-whisker plot visually displays the minimum value, the...
4 more steps in this tutorial
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Sign Up Free to ContinueSample Practice Questions
Easy
In a box-and-whisker plot, which value is represented by the vertical line inside the box?
A.The Mean
B.The Median (Q2)
C.The Interquartile Range (IQR)
D.The Maximum
Easy
A box-and-whisker plot for student test scores has a line inside the box at the value 80. What does this line represent?
A.The minimum score
B.The median score
C.The maximum score
D.The first quartile (Q1)
Easy
A box-and-whisker plot shows the number of points scored by a basketball player per game. The plot has a maximum value of 45. What does this value represent?
A.The player scores 45 points in most games.
B.The average number of points the player scores is 45.
C.The highest number of points the player scored in a single game was 45.
D.Half of the games, the player scored more than 45 points.
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