Box and Whisker Plots
Name: ___________________
1. Just the Math: Box – and – Whisker Plots A box-and-whisker plot (also known as a box
plot) is used to represent a large data set. Box-and-whisker plots allow you to easily make
comparisons of data sets. The box-and-whisker plot below represents a set of data.
What do you think is the lower extreme of the data set? What do you think is the upper
extreme? Use complete sentences in your answer.
The vertical line inside the box represents the second quartile Q2 of the data. What is the value
of Q2? Use a complete sentence in your answer.
The point in the box directly to the left of the second quartile represents the first quartile Q 1.
What is the value of Q1? Use a complete sentence in your answer.
Similarly, the point in the box directly to the right of the second quartile represents the third
quartile Q3? What is Q3? Use a complete sentence in your answer.
The horizontal lines on both ends of the box are called whiskers. What do the dots at the end of
the whiskers represent? Use a complete sentence in your answer.
2. To create a box-and-whisker plot of the cereal data use the extremes and quartiles that you
found. Complete the information below.
Draw a number line below and label it to represent the full
range of data values. Locate the second quartile on the
number line. About an inch above the number line, draw a dot
for Q2 and label its value. Repeat this process to draw dots for
the first and third quartiles and for the upper and lower
extremes. Then draw a box with sides at the first and third
quartiles. Draw a vertical line through the median. Draw two whiskers from the sides of the box
to the extremes.
Lower Extreme
First Quartile, Q1
Second Quartile, Q2
Third Quartile, Q3
Upper Extreme
3. From the box and whisker plot above, (the one created in #2) why is one whisker longer than
the other? What does this mean? Use a complete sentence in your answer.
4. An outlier is a data value that is much greater than or much less than the other values in the
set. What is the outlier in the breakfast cereal data? Make a conjecture, or an educated guess,
about which quartile would be the most affected by removing the outlier. Write your answer
and your conjecture using complete sentences.
5. Remove the outlier and
find the values of the
quartiles. Complete the
table to see if you were
correct.
Original Data
Data with outlier removed
First Quartile
Second Quartile
Third Quartile
6. Quartiles divide the data set into four parts. Percentiles also divide the data set into parts.
Based on the root of this word, into how many parts do you think percentiles divide the data
set? Use a complete sentence in your answer.
The nth percentile for the data set is the value for which n percent of the numbers in the set are
less than that value. For example, the median in a data set often represents the 50 th percentile
because 50% of the data are less than the median. In the original cereal data set, is the median
the 50th percentile? Use a complete sentence in your answer.
What percentile ranking is the first quartile in this data set? Use a complete sentence to explain
your reasoning.
The third quartile represents what percentile in this data set? Explain your answer using a
complete sentence.
7. The interquartile range, or IQR is the difference between the upper and lower quartiles
(Q3 – Q1) and represents the range of approximately the middle 50% of the data. The IQR
indicates the spread between the lower and upper quartiles. If it is a small number, then the
middle 50% of the data are consistent. If it is a large number, then the middle 50% of the data
are spread apart. Find the IQR for the original cereal data.