Practice Questions for Chapter 3
Numerical Descriptive Measures
1.
The times (in minutes) taken by a sample of nine students to complete a statistics
test are:
a) Find the Mean, Median, and Mode.
b) Calculate the 10% trimmed mean for these data
c) Calculate the range, variance, standard deviation, and coefficient of variation
2.
The mean age of five members of a family is 40 years. The ages of four of the five
members are 61, 60, 27, and 23 years. What is the age of the fifth member?
3.
The waiting times (in minutes) for 11 customers at a supermarket are:
a. Find the three quartiles and the IQR.
b. What is the approximate value of the 60th percentile for this data
c. What is the percentile rank for the customer who waited 11 minutes
4.
The following table gives the frequency distribution of prices for all 30 cellphone cases
sold in the college bookstore.
Price
20 to less than 30
30 to less than 40
40 to less than 50
50 to less than 60
60 o less than 70
f
4
7
12
4
3
a. What is the standard deviation of the prices of cellphone cases, rounded to two decimal
places?
b. According to Chebyshev's theorem, what is the minimum percentage of values that fall
within 2 standard deviations of the mean?
5.
6(i.)
The following data represents the ages of 15 people buying lift tickets at a ski area.
a. Calculate the key measures of center and dispersion.
b. Are there any outliers in this data set? If so, what are they, and are they mild or
extreme outliers?
The mean age of all high school teachers in City A is 42 years, and the standard
deviation is 6 years. According to Chebyshev's theorem, what percentage of teachers
in City A are between 24 and 60 years old?
6(ii.)
The ages of all high school teachers in the city have a bell-shaped distribution with a
mean of 38 years and a standard deviation of 4 years. According to the empirical rule,
what is the percentage of teachers in City C who are 34 to 42 years old?
7.
Here is a dot plot of migraine intensity (on a scale of 1 to 10) for 29 adults suffering from
recurring migraines.
What is the 5-number summary for this data set?
8.
A dataset of 1,000 exam scores has a mean of 72 and a standard deviation of 8.
a) Using Chebyshev’s theorem, find the minimum percentage of scores that lie between
56 and 88.
b) Compare your result with the empirical rule if the distribution is approximately
normal.
c) Explain why Chebyshev’s theorem always provides a weaker guarantee than the
empirical rule.
9(i.)
9(ii.)
10.
Data concerning the time between failures (in hours of operation) for a computer
printer have been recorded, and the first quartile equals 42 hours, the second quartile
equals 54 hours, and the third quartile equals 86 hours. What is the value of the lower
inner fence?
Data concerning the time between failures (in hours of operation) for a computer
printer has been recorded, and the first quartile equals 34 hours, the second quartile
equals 60 hours, and the third quartile equals 76 hours. What is the value for the
upper inner fence?
Based on the box-and-whisker plot,
Complete the table.
Minimum
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Median
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Maximum
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0
