Investigation: Data Display- Box Plots with Resting Heart Rates
Appendix
In this investigation you will
 find five-number summaries for data sets
 interpret and create box plots
 draw conclusions about a data set based on graphs and summary values
A box plot or box and whisker plot is a visual display of data and shows the five number
summary. This type of display shows the spread of the data. Look at the example of a box plot
below.
Minimum or
Lower Extreme
Maximum or
Upper Extreme
The five-number summary uses five boundary points: the minimum (the smallest value), the
maximum (the largest value), the median (which divides the data in half), the first quartile (the
median of the first half of the data), the third quartile (the median of the second half of the
data).
The first quartile (Q1), the median, and the third quartile (Q3) divide the data into four equal
groups. Twenty-five percent of the data lies between the minimum and Q1. Twenty-five
percent of the data lies between Q1 and the median. Twenty-five percent of the data lies
between the median and Q3. Twenty-five percent of the data lies between the Q3 and
maximum.
Statisticians are concerned about the middle 50% of the data. This is defined as the
interquartile range. To determine the interquartile range subtract the value of Q1 from Q3.
Q3 - Q1 = interquartile range.
Step 1: Record the resting heart rate for every student in the class.
Student 1 _____
Student 2 _____
Student 3 _____
Student 4 _____
Student 5 _____
Student 6 _____
Student 7 _____
Student 8 _____
Student 9 _____
Student 10 _____
Student 11 _____
Student 12 _____
Student 13 _____
Student 14 _____
Student 15 _____
Student 16 _____
Student 17 _____
Student 18 _____
Student 19 _____
Student 20 _____
Student 21 _____
Student 22 _____
Student 23 _____
Student 24 _____
Student 25 _____
Student 26 _____
Student 27 _____
Student 28 _____
Step 2: Put the data in order from smallest to largest. Indentify the lowest pulse rate. This
value is the minimum or lower extreme. Minimum: ___________ Indentify the highest pulse
rate. This value is the maximum or upper extreme. Maximum: ____________
Step 3: Determine the median. The median is the middle value in your list of numbers. It
divides the data into two halves. If you have an odd number of students in your class, then the
median is an actual point or value. If you have an even number of students in the class, the
median is the average of the two middle values in your data.
The formula for the place to find the median is "([the number of data points] + 1) ÷ 2", but you
don't have to use this formula. You can just count in from both ends of the list until you meet in
the middle, if you prefer. Either way will work.
Median: ____________
Step 4: Now you will determine Q1 and Q3.
The median divides your data into two halves. Quartile 1 is the median of the lower half of your
data. Note: If the median falls between two data points, then the lower point is considered
part of the lower half of the data and the upper point is part of the upper half of the data.
Q1:____________ Determine Q3 by determining the median of the upper half of the data.
Q3____________
Page 3 Appendix
Step 5: Construct a box plot using your data.
 Use a clean sheet of paper to draw a number line with a consistent scale. The
number line should start below the minimum and extend past the maximum.
 Find the median value on your number line and draw a short vertical line
segment just above it. Repeat this process for the first and third quartile.
 Place dots above your number line to represent the minimum and maximum
values.
 Draw a rectangle with ends at the first and third quartiles. This is the box.
 Draw horizontal segments that extend from each end of the box to the minimum
and maximum values. These are called the whiskers.
The difference between the first quartile and third quartile is the interquartile range, or IQR.
Like the range, the interquartile range helps describe the spread of the data.
Step 6: Answer the questions below.
a.
b.
What are the range and IQR of your data?
How many pulse rates fall between the first and third quartiles of the graph?
What fraction and percentage of the total number of pulse rates is this number? Will
this fraction and percentage always be the same?
Data that are more than 1.5 times the interquartile range beyond the quartiles are called
outliers.
 First determine the IQR
 IQR - 1.5(Q1) will determine the outliers for the lower part of the data.
 IQR + 1.5(Q3) will determine the outlier for the upper part of the data.
Outliers are not connected to the whiskers.
Step 7: Determine if any outliers exist in the data. Interpret what this would mean for our data
set.