Chapter 4—Measures of Central Tendency
MULTIPLE CHOICE QUESTIONS
4.1 The best measure of central tendency
4.2 + For the following set of data [5 9 5 5 2 4], the mean is
4.3 + If we were interested in studying salaries in the National Basketball Association,
the least useful measure of the typical salary would be
4.4 The median has at least one advantage over the mean in that
4.5 The median location is
4.6 In which of the following situations would you be most likely to use the mean as a
measure of central tendency?
Chapter 4
4.7 + Which of the following is useful with data collected with nominal scales?
4.8 + Which of the following statements about the mode is false?
4.9 + The mode of the numbers 1 3 4 5 6 6 7 8 9 9 9 is
4.10 + We are most likely to randomly pick which score from an actual data set?
4.11 + Given the numbers 6 7 9 11 15 71 86, how many numbers fall below the
median?
4.12 The median location is defined as
4.13 The chief advantage of the median is that
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4.14 The chief disadvantage of the median, when compared to the mean, is that
4.15 The most commonly used measure of central tendency is
4.16 + When the distribution is symmetric, which of the following are always equal?
4.17 When the distribution is symmetric and unimodal, which of the following are
always equal?
4.18
X
is the symbol commonly used for the
4.19 + In using ordinal data, which measure of central tendency is probably least useful?
4.20 + The measure of central tendency that is most useful in estimating population
characteristics because it is less variable from sample to sample is the
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4.21 Suppose a sample of children reported how many voices they heard in their heads
on a particular day, and that hearing voices was a relatively uncommon
experience. In this case the mode
4.22 Alison received a score of 480 on the verbal portion of her SAT. If she scored at
the 50th percentile, her score represents the _______ of the distribution of all
verbal SAT scores.
4.23 Which of the following measures of central tendency is potentially misleading if
the data are collected on an ordinal scale?
4.24 + On a histogram, which always refers to the highest point on the distribution?
4.25 Which of the following is NOT a disadvantage of the mean?
4.26 + For the data set [1, 3, 3, 5, 5, 5, 7, 7, 9], the value “5” is
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4.27 + For the following data set [1, 7, 9, 15, 33, 76, 103, 118], what is the median
location?
4.28 For the following data set [1, 9, 9, 9, 11, 28], which of the following is false?
4.29 + Which of the following can be defined algebraically?
4.30 Professor Neuberg found that the mean number of alcoholic drinks consumed at a
party was much higher for males than for females. If the median and mode
number of drinks consumed by males and females was both zero, how can the
difference in means be explained?
4.31 Which of the following is true of the value “9” in the following data set [1, 1, 1, 7,
9, 12, 15, 65, 100]?
4.32 + If a store manager wanted to stock the men’s clothing department with shirts
fitting the most men, which measure of central tendency of men’s shirt sizes
should be employed?
Chapter 4
4.33 If a physics professor gave her class the same exam every year, which of the
following measures of exam scores would probably stay the most consistent in
value from year to year?
4.34 When we make implicit assumptions about a scale having interval properties,
4.35 Which of the following is probably most useful in studies in which extreme scores
sometimes occur but have no real practical significance?
TRUE/FALSE QUESTIONS
spread of a distribution.
50% of the scores fall when the data is arranged in numerical order.
central tendency.
4.40 [FALSE] The median is typically more stable from sample to sample than the
mean.
number of values.
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than are the median or mode.
OPEN-ENDED QUESTIONS
4.46 Answer the following questions based on this set of numbers:
1 2 2 3 3 3 4 5
a) What is the mean?
b) What is the median?
c) What is the mode?
4.47 The following are test grades from the first statistics exam. Briefly describe the
data, including each of the 3 measures of central tendency.
45 50 65 65 70 70 75 80 85 90 95
100
4.48 Answer the following questions based on this graph.
18.017.016.015.014.013.012.011.0
Frequency
5
4
3
2
1
0
a) What is the median?
b) What is the mode?
c) What is a reasonable estimate of the mean? Explain your estimate.
4.49 A sample of 20 families reported how many children they have. Answer the
following questions based on the summary table below.
Number of children
0
1
2
3
4
Number of families
3
6
7
3
1
a) What is the mean?
b) What is the median?
c) What is the mode?
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4.50 A resident assistant was interested in the cigarette consumption in her dormitory.
After conducting a survey with 700 residents, she reported that, on average,
residents smoked 5 cigarettes a day. This statistic included the data from 400
students who claimed to smoke 0 cigarettes a day. What would be a more
appropriate way to describe the cigarette consumption of smokers?
4.51 A seasonal convenience store currently sells laundry detergent in three standard
size containers. Due to limited shelf space, they want to offer only one size in the
future. They have the sales record for each size over the previous year. Which
measure of central tendency would best help them decide which size to stock in
the future? Explain your answer.
4.52 A researcher recorded the gender of his participants as follows: 1=Male and
2=Female. Which measure of central tendency would be most useful to describe
the gender of his sample? Explain your answer.
4.53 Given the following data set, demonstrate that multiplying the mean by a constant
of 2 is equivalent to multiplying each value by that constant (2) and then
calculating the mean.
1 2 3 4
4.54 Given the following distributions, which measure of central tendency would be
the largest value?
a) Negatively skewed
b) Positively skewed
4.55 What is the relationship between the mean, median, and mode in a symmetrical
distribution?
Answers to Open-ended Questions
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