Mathematics
Grade 7
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, first quartile, median, third quartile, maximum) from a box-and-whisker plot.
Locate and interpret the median, quartiles, and extreme values on a box-and-whisker plot.
Calculate the interquartile range (IQR) from a given box-and-whisker plot.
Compare and contrast the central tendency and spread of two or more data sets represented by box-and-whisker plots.
Describe the distribution of data within each section of a box-and-whisker plot, understanding that each section represents 25% of the data.
Use box-and-whisker plots to answer questions about data sets, such as the percentage of data above or below a certain point.
Ever wonder how to quickly compare test scores from two different classes or track a sports team...
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Key Concepts & Vocabulary
TermDefinitionExample
Box-and-Whisker PlotA graph that displays the five-number summary of a set of data. It visually shows the spread and center of the data, making it easy to compare distributions.A box-and-whisker plot for student test scores might show that most students scored between 70 and 90, with a few very high or very low scores.
Five-Number SummaryThe five key values that summarize a data set: the minimum value, the first quartile (Q1), the median (Q2), the third quartile (Q3), and the maximum value.For the data set {1, 3, 5, 7, 9}, the five-number summary is (1, 3, 5, 7, 9).
Median (Q2)The middle value of a data set when it is ordered from least to greatest. It divides the data into two equal halves, with 50% of the data below it and 50% above it.In the data set {10, 12, 15,...
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Core Formulas
Interquartile Range (IQR) Calculation
$IQR = Q_3 - Q_1$
Use this rule to find the spread of the middle 50% of your data. A larger IQR means the middle data is more spread out, while a smaller IQR means it's more clustered around the median.
Data Distribution by Quartiles
Each of the four sections of a box-and-whisker plot (whisker to Q1, Q1 to Median, Median to Q3, Q3 to whisker) represents 25% of the data.
This rule helps you understand how data is distributed. For example, 50% of the data falls between Q1 and Q3 (the box), and 75% of the data is below Q3.
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Challenging
A data set has a median of 60, an IQR of 30, and a maximum value of 100. The value for Q1 is 50. Which of the following box plots could represent this data?
A.plot with a box from 50 to 80 and a median at 60.
B.plot with a box from 60 to 90 and a median at 75.
C.plot with a box from 50 to 100 and a median at 60.
D.plot with a box from 30 to 60 and a median at 50.
Challenging
Box plots for the heights of players on the basketball team and the soccer team are shown. Basketball: (Q1=70, Med=73, Q3=76). Soccer: (Q1=66, Med=68, Q3=71). Which statement is guaranteed to be true?
A.The tallest soccer player is shorter than the shortest basketball player.
B.At least 75% of the basketball players are taller than the median height of the soccer players.
C.The average height of the basketball players is 5 inches more than the soccer players.
D.The basketball team has a wider range of heights than the soccer team.
Challenging
A teacher wants to know which of her two classes had more consistent scores on a test. Class A's scores have an IQR of 12 and a range of 40. Class B's scores have an IQR of 15 and a range of 30. Which class was more consistent and why?
A.Class B, because its overall range is smaller.
B.Class A, because its Interquartile Range (IQR) is smaller.
C.Both classes were equally consistent.
D.Class A, because its overall range is larger.
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