Descriptive Statistics Homework
Answer each of the following questions. Start a new question on a new page. No matter
how you compute the statistics always include the appropriate formula. Be sure to round
your final answers.
Q1. Neftali Feliz Fastballs
Neftali Feliz is the closing pitcher for the Texas Rangers. During a recent relief appearance he threw 5
fastballs. They were clocked at 93, 98, 94, 96, 93, and 96 miles per hour. Consider this data to be a
sample from a random process. Do the following by hand or with your calculator using the statistical
functions or by hand using the table technique. Then check your answers with StatCrunch. You will be
required to do this on your exam.
Q1.1
Draw a dot plot of the sample data. Use StatCrunch to draw this plot.
Q1.2
Compute the arithmetic mean speed of the fast balls. (Partial Answer: 95.0 mph)
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Descriptive Statistics Homework
Q1.3
Compute the median speed of the sample. (Partial Answer: 95.0 mph)
Q1.4
Compute the mode of the sample. (No partial answer. Why?)
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Descriptive Statistics Homework
Q1.5
Compute the variance of the sample. (Partial Answer: 4.0 mph2)
Q1.6
Compute the standard deviation of the sample. (Partial answer: 2 mph)
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Descriptive Statistics Homework
Q1.7
Compute the coefficient of variation of the sample. What does this tell you about Feliz’s consistency?
(Partial Answer: 2.1%)
Q1.8
The speed of the fastball thrown by Feliz is mound shaped. Use the 2SD rule to estimate the interval
such that 95% of the observations fall in that interval. Carry out your computations to 1 decimal place.
(Partial answer: 91.0 mph – 99.0 mph )
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Descriptive Statistics Homework
Q2: UTA women’s Basketball
The data set named 2010-2011 UTA Women's Basketball Team is available on StatCrunch. Load this
data set. The variable we are interested in is the player’s height (inches)
Q2.1
Use StatCrunch and draw a dot plot and a stem-and-leaf plot of the distribution of the heights the
basketball team. What do these tell you? (No partial answer)
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Descriptive Statistics Homework
Q2.2
Compute and interpret the mean, median, and mode of the height of the UTA women’s basketball team.
Use StatCrunch to carry out the computations. Can you infer the skewness from the values of the mean
and mode? If so how? (Partial answer: 69.4 inches, 70 inches, no mode ).
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Descriptive Statistics Homework
Q2.3
Compute and interpret the range, the inter-quartile range, the variance, and the standard deviation of
UTA women’s basketball team. (Partial Answer: 5 inches, 9.8 inches2, 3.1 inches)
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Descriptive Statistics Homework
Q 2.4
Assume the data is mound shaped. Compute the upper and lower limits using the 2SD rule. Provide the
appropriate interpretation of the rule in the context of the data. (Partial answer: 63.2 inches, 75.6
inches )
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Descriptive Statistics Homework
Q3: Comparing the Variation of the UTA Men and Women’s Basketball
Team
Q3.1
Use StatCrunch and draw a dot plot and a stem-and-leaf plot of the distribution of the heights the
basketball team. What do these tell you? (No partial answer)
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Descriptive Statistics Homework
Q3.2
Compute and interpret the mean, median, and mode of the height of the UTA women’s basketball team.
Use StatCrunch to carry out the computations. Can you infer the skewness from the values of the mean
and mode? If so how? (Partial answer: 76.6 inches, 77.0 inches, 77 inches ).
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Descriptive Statistics Homework
Q3.3
Compute and interpret the range, the inter-quartile range, the variance, and the standard deviation of
UTA women’s basketball team. (Partial Answer: 3 inches, 14.1 inches2, 3.8 inches)
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Descriptive Statistics Homework
Q 3.4
Assume the data is mound shaped. Compute the upper and lower limits using the 2SD rule. Provide the
appropriate interpretation of the rule in the context of the data. (Partial answer: 69.0 inches, 84.2
inches )
Q3.5
Which of the two distributions have the greatest variability with respect to the mean? Show your work.
(No partial answer)
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Descriptive Statistics Homework
Q4: Children with Special Healthcare Needs
The StatCrunch Percent Children with Special Care Needs gives the percent of children for ages 1
through 17 who have special healthcare needs in each state and Washington, D.C.
Q4.1
Draw a histogram and a boxplot of the percent of children with special health care needs. Summarize
your findings.
Q4.2
Draw a statistical map of the percent of children who have special healthcare needs. This routine can be
found under the Graphics Menu.
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Descriptive Statistics Homework
Q4.3
Compute and report the standard statistics we use to summarize statistical distributions. Be sure to
round your answers appropriately.
Q4.4
Summarize your finds in short paragraph. Did you find anything surprising?
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