Chapter 4
#5
5. The histogram shows the lengths of hospital stays (in days) for all the
female patients admitted to hospitals in New York in 1993 with a
primary diagnosis of acute myocardial infarction (heart attack).
a) Describe the distribution’ SHAPE.
The distribution is skewed to the
right and possibly bimodal
Chapter 4
#5
5. The histogram shows the lengths of hospital stays (in days) for all the
female patients admitted to hospitals in New York in 1993 with a
primary diagnosis of acute myocardial infarction (heart attack).
b) Describe the distribution’s Outliers and
unusual features.
The distribution has a gap at 35
days with a possible outlier at 36
days.
Chapter 4 #14a
The Cornell Lab of Ornithology
holds an annual Christmas Bird
Count, in which birdwatchers
at various locations around the
country see how many
different species of birds they
can spot. Here are some of the
counts reported from sites in
Texas during the 1999 event.
228
178
186
162
206
166
163
183
181
206
177
175
167
162
160
160
157
156
153
152
a) Create a stem-and-leaf display
of these data.
Chapter 4 #14b
b) Write a brief description of the
distribution. Be sure to discuss the
overall shape, center, spread,
and any outliers.
The distribution is skewed right. There are
possible high outliers at 206 and 228
birds. The center is at the median of 166
birds with an IQR of 23.5 birds.
Q1 = 158.5 (between 5th & 6th from LOW end)
Q3 = 182 (between 5th & 6th from HIGH end)
Chapter 5 #12&14
12&14. Below is a stem-and-leaf display of the number of games played
by hockey great Wayne Gretzky during his 20-year career in the NHL.
a) Would you use the median or the
mean to describe the center of this
distribution? Why?
We should use median. The distribution is
skewed to the left, and has low outliers.
The median is more resistant to the
skewness and outliers than the mean.
Chapter 5 #12&14
12&14. Below is a stem-and-leaf display of the number of games played
by hockey great Wayne Gretzky during his 20-year career in the NHL.
b) Find the median.
The median is 79 games.
Both the 10th and 11th values are 79, so
the median is the average of these two,
also 79.
Chapter 5 #12&14
12&14. Below is a stem-and-leaf display of the number of games played
by hockey great Wayne Gretzky during his 20-year career in the NHL.
c) Without actually finding the
mean, would you expect it to be
higher or lower than the median?
Explain.
The mean should be lower. There are two
seasons when Gretzky played an unusually
low number of games. Those seasons will
pull the mean down.
Chapter 5 #12&14
12&14. Below is a stem-and-leaf display of the number of games played
by hockey great Wayne Gretzky during his 20-year career in the NHL.
d) Find the range. (Show your work.)
The range is the distance between the
minimum and maximum.
82 – 45 = 37 games.
(NOTE: Range is a measure of SPREAD.)
Chapter 5 #12&14
12&14. Below is a stem-and-leaf display of the number of games played
by hockey great Wayne Gretzky during his 20-year career in the NHL.
e) Find the interquartile range. (Circle Q1
and Q3 on the stem-and-leaf display first
and then show work.)
𝟖𝟎 + 𝟖𝟎
𝑸𝟑 =
= 𝟖𝟎
𝟐
𝟕𝟑 + 𝟕𝟒
𝑸𝟏 =
= 𝟕𝟑. 𝟓
𝟐
𝑰𝑸𝑹 = 𝑸𝟑 − 𝑸𝟏
= 𝟖𝟎 − 𝟕𝟑. 𝟓
= 𝟔. 𝟓 𝒈𝒂𝒎𝒆𝒔
Chapter 5 #12&14
12&14. Below is a stem-and-leaf display of the number of games played
by hockey great Wayne Gretzky during his 20-year career in the NHL.
f) Using the Outlier Rule, explain why the
two seasons when Gretzky played only 45
and 48 games could be considered outliers.
Lower Fence: 𝑄1 – 1.5(IQR)
= 73.5 – 1.5(6.5)
= 73.5 – 9.75
= 63.75
Both the 45 game season and the 48
game season are well below the fence,
so they could be considered outliers.
Chapter 5 #12&14
12&14. Below is a stem-and-leaf display of the number of games played
by hockey great Wayne Gretzky during his 20-year career in the NHL.
g) Do you consider the 64-game season an
outlier, too? Explain.
The 64 game season is very close to
the lower fence of 63.75. Technically it
is not outside the fence, so it isn’t an
outlier.
Chapter 5 #36
36. The Farmingham Heart Study recorded the cholesterol levels of
more than 1400 men. Here is an ogive of the distribution of these
cholesterol measures. (An ogive is a cumulative frequency graph that
shows the percentage of cases at or below a certain value.)
75%
Max
a) Construct a boxplot for these data.
50%
25%
Min
Max is about 420.
Min is about 100.
Q3 is about 260.
Median is about 230.
Q1 is about 200.