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Lesson 2.1
LESSON OVERVIEW VIDEO
Watch the Lesson 2.1–2.3 overview
video for guidance from the authors on
teaching the content in these lessons.
Find it by clicking on the link in the
TE-book or by logging into the teachers’
resources on our digital platform.
LEARNING T AR GET KEY
The problems in the test bank are
(C) 2021 BFW Publishers -- for review purposes only.
keyed to the learning targets using
these numbers:
• 2.1.1
• 2.1.2
• 2.1.3
TEACHING TIP:
Learning Targets
Learning targets are featured at the start
of every lesson. Each learning target
has one corresponding example in the
lesson and corresponding exercises at
the end of each lesson. Use the learning
targets to focus student attention on the
statistical content of the lesson.
BELL RINGER
Your family doctor tells you that you are
at the 80th percentile for height. What
do you think she means?
FYI
Students have probably encountered
percentiles in two places: standardized
test results and doctor’s offices. The 90
SAT, ACT, and other major standardized
tests give percentile rankings for scores.
When getting annual checkups, the
height and weight of a child (relative to
other children of the same age) are often
given as percentiles. For growth charts The title of this lesson is Describing Location
from the Centers for Disease Control and
Prevention (CDC) that use percentiles, location of one value relative to the other
search the Internet for “CDC clinical values in the distribution.
growth charts.”
90 CHAPTER 2 • Modeling One-Variable Quantitative Data
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Describing Location
in a Distribution
L E AR N I N G TAR G E T S
• Find and interpret a percentile in a distribution of quantitative data.
• Find and interpret a standardized score ( z -score) in a distribution
of quantitative data.
• Use percentiles or standardized scores ( z -scores) to compare the location
of values in different distributions.
Here are the scores of all 25 students in Mr. Pryor’s statistics class on their first test:
79 81 80 77 73 83 74 93 78 80 75 67 73
77 83 86 90 79 85 83 89 84 82 77 72
The bold score is Jenny’s 86. How did she perform on this test relative to her classmates?
The following dotplot displays the class’s test scores, with Jenny’s score marked in
red. The distribution is roughly symmetric with no obvious outliers. From the dotplot,
we can see that Jenny’s score is above the mean (balance point) of the distribution.
We can also see that Jenny did better on the test than most other students in the class.
d d d d d d d
d d dd d d dddddd dd d dd d
65 70 75 80 85 90 95
Score
Finding and Interpreting Percentiles
One way to describe Jenny’s location in the distribution of test scores is to calculate
Q
,
Q
her percentile. Recall that the three quartiles ( 1 median, 3 ) divide a distribution of
quantitative data into four roughly equal size groups. The idea of a percentile is sim-
ilar: the 99 percentiles divide a distribution into 100 roughly equal size groups. This
idea makes sense if a quantitative data set has a large number of values, but breaks
down for smaller data sets.
DEFINITION Percentile
An individual’s percentile is the percent of values in a distribution that are less than the
individual’s data value.
Using the dotplot, we see that Jenny’s 86 places her fourth from the top of the
class. Because 21 of the 25 data values (84%) are less than her score, Jenny is at the
caution 84th percentile in the class’s distribution of test scores.
! Be careful with your language when describing percentiles. Percentiles are specific
aution
locations in a distribution, so an observation isn’t “in” the 84th percentile. Rather, it
is “at” the 84th percentile.
One other important note: percentiles are usually reported as whole numbers.
Consider a quantitative data set with 43 values. How should we report the percentile
for the individual with 30 of the 43 values in the distribution less than their data
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TEACHING TIP
There is no universally agreed-upon definition
in a Distribution. The location of what? The for percentile. Although the examples and
solutions in this textbook will stick with
the “less than” definition given here, some
students may use the “less than or equal to”
definition to compute percentiles. We don’t
recommend penalizing students for using the
“less than or equal to” definition.
10/11/20 7:42 PM