Mathematics
Grade 6
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 key numbers (minimum, first quartile, median, third quartile, maximum) from a box-and-whisker plot.
Determine the median, which represents the middle value of a data set, from a box-and-whisker plot.
Calculate the range of a data set using the minimum and maximum values shown on a box-and-whisker plot.
Calculate the interquartile range (IQR) by finding the difference between the first and third quartiles from a box-and-whisker plot.
Describe the spread and central tendency of a data set based on the visual representation of a box-and-whisker plot.
Compare and contrast two different data sets by interpreting their respective box-and-whisker plots.
Ever wonder how to quickly compare a whole bunch of numbers, like test scores or daily tempe...
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Key Concepts & Vocabulary
TermDefinitionExample
Box-and-Whisker PlotA type of graph that displays the five-number summary of a set of data: minimum, first quartile (Q1), median, third quartile (Q3), and maximum. It shows the spread and center of the data.A plot showing student test scores from 60 to 100, with a box in the middle and lines extending outwards.
Minimum ValueThe smallest number in a data set, represented by the end of the left whisker on a box-and-whisker plot.If the left whisker ends at 5, the minimum value is 5.
Maximum ValueThe largest number in a data set, represented by the end of the right whisker on a box-and-whisker plot.If the right whisker ends at 95, the maximum value is 95.
Median (Q2)The middle value of a data set when it's ordered from least to greatest. It divides the data into two...
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Core Formulas
Identifying the Five-Number Summary
The box-and-whisker plot visually represents the minimum, first quartile (Q1), median (Q2), third quartile (Q3), and maximum values of a data set.
Minimum: Leftmost point of the left whisker. Q1: Left edge of the box. Median: Line inside the box. Q3: Right edge of the box. Maximum: Rightmost point of the right whisker.
Calculating the Range
$\text{Range} = \text{Maximum Value} - \text{Minimum Value}$
Use this rule to find the total spread of the entire data set, from the smallest to the largest value.
Calculating the Interquartile Range (IQR)
$\text{IQR} = \text{Q3} - \text{Q1}$
Use this rule to find the spread of the middle 50% of the data, which is represented by the length of the box.
5 more steps in this tutorial
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Challenging
A box plot of weekly allowances has a range of $15 and a maximum value of $20. The interquartile range is $6 and the third quartile (Q3) is $14. What is the first quartile (Q1)?
A.$5
B.$8
C.$9
D.$2
Challenging
A box plot shows company salaries. The median is $50,000. The box is very short (Q1=$48k, Q3=$53k) but the right whisker is extremely long, ending at a maximum of $250,000. Which is the best interpretation?
A.Salaries are evenly spread from the minimum to the maximum.
B.Most employees earn a very high salary.
C.The majority of employees earn salaries clustered close to $50,000, but a few executives earn much higher salaries.
D.The data is incorrect because the maximum is too far from the median.
Challenging
On a box plot of house prices in a town, the median is very close to Q3, but far from Q1. What does this suggest?
A.Most houses are very expensive, with a few inexpensive ones.
B.House prices are evenly distributed across the entire range.
C.large percentage of houses are clustered at the higher end of the price range.
D.large percentage of houses are clustered at the lower end of the price range.
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