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Matching Shapes to Characteristics Activity
Distribution 1
Distribution 2
Characteristic =
Characteristic =
Distribution 3
Distribution 4
Characteristic =
Characteristic =
Characteristics:
1. Distribution of age for the population of the United States in the year 1980.
Describe and explain the shape of the distribution.
2. Distribution of miles of coastline for the 50 United States.
Describe and explain the shape of the distribution.
Which states do you think would be in the last class furthest to the right?
3. Distribution of the number of miles traveled to work, that is,
commuting distance for employed adults in a city.
Describe and explain the shape of the distribution.
4. Distribution of age at death for the population of the United States (year 1980).
Describe and explain the shape of the distribution.
Increasing Spread Activity
Consider the following three data sets.
I: 20 20 20
II: 18 20 22
III: 17 20 23
(a) Which data set will have the smallest standard deviation?
(b) Which data set will have the largest standard deviation?
(c) Find the standard deviation for each data set and
check your answers to (a) and (b).
Check for Nonnormal Features Activity
The following frequency plots display distributions of samples of hypothetical exam scores,
two of which were drawn from populations which are normally distributed. Identify the three
samples which do not come from normal populations, and explain in each case why the
sample is clearly nonnormal.
(a) Distribution for Exam __________ is nonnormal because:
(b) Distribution for Exam __________ is nonnormal because:
(c) Distribution for Exam __________ is nonnormal because:
Comparing Distributions Activity
Consider the following three distributions.
The mean and standard deviation for each distribution are also provided.
(a) Is Distribution A symmetric?
YES
NO
Is Distribution B symmetric?
YES
NO
Is Distribution C symmetric?
YES
NO
(b) For each distribution, find the proportion of values that are within one standard deviation
of the mean.
Distribution A [  ] =
Proportion in this range =
Distribution B [  ] =
Proportion in this range =
Distribution C [  ] =
Proportion in this range =
(c) Which distributions have 68% of the values within one standard deviation of the mean?
Note: There are many types of distributions and not all distributions are normal. Knowing that a distribution
is symmetric does not imply it will follow the 68-95-99.7 rule.
Usefulness of Randomization Activity
Consider a study to compare two antibiotics for treating strep throat in children, Amoxicillin
and Cefadroxil. At one center for this study, 23 children (who met the study entrance criteria
and for whom consent was given) were randomly assigned to one of the two treatment
groups. One concern is that age of the child might influence the effectiveness of the
antibiotics. The ages of the children in each treatment group are given below. Calculate the
mean, median, and mode for each of the two treatment groups. How do the two groups
compare with respect to age?
How do the two groups compare with respect to age?
Give the five-number summary for each group. Comment on your results.
Amoxicillin Group (n=11):
8
9
9
10
7
8
9
9
10
11
11
12
14 14
17
Five-number summary:
Cefadroxil Group (n=12):
9
10
Five-number summary:
Make side-by-side boxplots for the antibiotic study data.
10 11
12
13
14
16