Chapter 4 #5 5. The histogram shows the lengths of hospital stays (in days) for all the female...

Chapter 4 #55. 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 #55. 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 #14aThe 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 #14bb) 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&1412&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.


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.


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.


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.)


e) Find the interquartile range. (Circle Q1 and Q3 on the stem-and-leaf display first and then show work.)

𝑸𝟑=𝟖𝟎+𝟖𝟎

𝟐=𝟖𝟎

𝑸𝟏=𝟕𝟑+𝟕𝟒

𝟐=𝟕𝟑 .𝟓


f) Using the Outlier Rule, explain why the two seasons when Gretzky played only 45 and 48 games could be considered outliers.

Lower Fence: – 1.5(IQR) = 73.5 – 1.5(6.5) = 73.5 – 9.75 = 63.75Both the 45 game season and the 48 game season are well below the fence, so they could be considered outliers.


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 #3636. 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.)

a) Construct a boxplot for these data.

50%

75%

25%

Min

Max

Q1 is about 200.

Max is about 420.Min is about 100.

Q3 is about 260.Median is about 230.

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