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Q:
7+ We generally like the standard deviation when we are trying to describe a sample of data because
a) it is larger than the variance.
b) it allows for more intuitive interpretation with respect to the data than does the variance.
c) it is less biased than the variance.
d) all of the above
Q:
6+ The population variance is
a) an estimate of the sample variance.
b) calculated exactly like the sample variance.
c) a biased estimate.
d) usually an unknown that we try to estimate.
Q:
5 A trimmed sample is one that
a) has been distorted by lopping off the highest scores.
b) is strongly influenced by outliers.
c) is unrepresentative of what it purports to measure.
d) has been truncated equally at the two extremes.
Q:
4 If we eliminate the top and bottom 25% of the data and take the range of what remains we have the
a) range.
b) adjusted range.
c) interquartile range.
d) quartile variance.
Q:
3+ An outlier
a) can be an extreme score.
b) can be an error that snuck into the data.
c) will never have a large influence on many measures of variability.
d) both a and b
Q:
2 Dispersion refers to
a) the degree to which data cluster toward one end of the scale.
b) the centrality of the distribution.
c) the degree to which individual data points are distributed around the mean.
d) all of the above
Q:
1+ Which of the following is NOT a measure of variability?
a) the density
b) the range
c) the standard deviation
d) the interquartile range
Q:
55 What is the relationship between the mean, median, and mode in a symmetrical distribution?
Q:
54 Given the following distributions, which measure of central tendency would be the largest value?
a) Negatively skewed
b) Positively skewed
Q:
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
Q:
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.
Q:
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.
Q:
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?
Q:
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?
Q:
48 Answer the following questions based on this graph. a) What is the median?
b) What is the mode?
c) What is a reasonable estimate of the mean? Explain your estimate.
Q:
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
Q:
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?
Q:
45 In general, the sample mean is a better estimate of the population mean than are the median or mode.
Q:
44 Algebraically, the mean = (ï“X)2/N.
Q:
43 A distribution can have more than one mode.
Q:
42 The median may fall between two numbers when there is an even number of values.
Q:
41 When the median falls between two numbers, the lower number is used.
Q:
40 The median is typically more stable from sample to sample than the mean.
Q:
39 The mean is more influenced by extreme scores than other measures of central tendency.
Q:
38 The mode is the most common value in a series of numbers.
Q:
37 The mean is the number that corresponds to the point at or below which 50% of the scores fall when the data is arranged in numerical order.
Q:
36 Measures of central tendency are used to describe the variability or spread of a distribution.
Q:
35 Which of the following is probably most useful in studies in which extreme scores sometimes occur but have no real practical significance?
a) mean
b) median
c) average
d) none of the above
Q:
34 When we make implicit assumptions about a scale having interval properties,
a) we are probably calculating a mode.
b) we are probably calculating a median.
c) we are assuming the distance between 4 and 6 is the same as the distance between 6 and 8.
d) we are always making unreasonable assumptions.
Q:
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?
a) mode
b) mean
c) median
d) none of the above
Q:
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?
a) mode
b) mean
c) median
d) average
Q:
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]?
a) It is the mode.
b) It is the mean.
c) It is the 50th percentile.
d) It is equal to (N+1)/2.
Q:
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?
a) The mean number of drinks consumed by females was disproportionately increased by outliers drinking lots of drinks.
b) The mean number of drinks consumed by males was disproportionately increased by outliers drinking lots of drinks.
c) The difference in means gives no information that is useful and should not be explained.
d) The difference most likely comes from an error in calculation.
Q:
29+ Which of the following can be defined algebraically?
a) mean
b) median
c) median location
d) both a and c
Q:
28 For the following data set [1, 9, 9, 9, 11, 28], which of the following is false?
a) The mode is 9.
b) The median is 9.
c) The mean is 9.
d) The median location is 3.5.
Q:
27+ For the following data set [1, 7, 9, 15, 33, 76, 103, 118], what is the median location?
a) 5
b) 4.5
c) 33
d) 24
Q:
26+ For the data set [1, 3, 3, 5, 5, 5, 7, 7, 9], the value "5" is
a) the mode.
b) the median.
c) the mean.
d) all of the above
Q:
25 Which of the following is NOT a disadvantage of the mean?
a) It is unduly influenced by extreme scores.
b) Its value many not actually exist in the data.
c) It is least stable from sample to sample.
d) Its interpretation in terms of variables requires some faith in the interval properties of the data.
Q:
24+ On a histogram, which always refers to the highest point on the distribution?
a) mean
b) median
c) mode
d) none of the above
Q:
23 Which of the following measures of central tendency is potentially misleading if the data are collected on an ordinal scale?
a) mean
b) median
c) mode
d) none of the above
Q:
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.
a) mean
b) median
c) mode
d) average
Q:
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
a) will show that the most common number of voices heard is zero.
b) will tell us nothing about the children who do hear voices.
c) both a and b
d) none of the above
Q:
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
a) mode
b) median
c) mean
d) All of the above are equally useful in estimating characteristics of the population.
Q:
19+ In using ordinal data, which measure of central tendency is probably least useful?
a) mode
b) mean
c) median
d) You cannot use any measure of central tendency with ordinal data.
Q:
18 is the symbol commonly used for the
a) mean.
b) mode.
c) median.
d) none of the above
Q:
17 When the distribution is symmetric and unimodal, which of the following are always equal?
a) mean and mode
b) median and mode
c) mean and median
d) mean, median, and mode
Q:
16+ When the distribution is symmetric, which of the following are always equal?
a) mean and mode
b) median and mode
c) mean and median
d) mean, median, and mode
Q:
15 The most commonly used measure of central tendency is
a) the mode.
b) the median.
c) the mean.
d) all are equally common
Q:
14 The chief disadvantage of the median, when compared to the mean, is that
a) it is less stable than the mean from sample to sample.
b) its location cannot be calculated algebraically.
c) it is disproportionately affected by outliers.
d) it has no disadvantages.
Q:
13 The chief advantage of the median is that
a) it represents a score actually occurring in the data set.
b) it is best used with nominal scales.
c) *it is not disproportionately affected by extreme scores.
d) it is the most commonly occurring score.
Q:
12 The median location is defined as
a) b) *
c) p(Xi=mode) > p(Xj=any other score)
d) the average score
Q:
11+ Given the numbers 6 7 9 11 15 71 86, how many numbers fall below the median?
a) 3
b) 11
c) 6 to 86
d) 6, 7, 9, and 11
Q:
10+ We are most likely to randomly pick which score from an actual data set?
a) the mode
b) the median
c) the highest score
d) the lowest score
Q:
9+ The mode of the numbers 1 3 4 5 6 6 7 8 9 9 9 is
a) 6
b) 6.5
c) 6.1
d) 9
Q:
8+ Which of the following statements about the mode is false?
a) It must be an actual score that occurred in the data set.
b) It can consist of more than one number.
c) It can be calculated algebraically.
d) All of the above are false.
Q:
7+ Which of the following is useful with data collected with nominal scales?
a) median
b) mode
c) mean
d) none of the above
Q:
6 In which of the following situations would you be most likely to use the mean as a measure of central tendency?
a) You want to report data on family income so we know how families are doing.
b) You want to measure something that has a number of outliers.
c) You want to report the average weight of airline passengers so that the pilot can estimate the weight of the plane.
d) Your boss wants to know what size T-shirts to order for the next company picnic.
Q:
5 The median location is
a) the number closest to the mean.
b) the number of scores that occur at the median.
c) the highest point on a frequency distribution.
d) the position, in an ordered series, occupied by the median.
Q:
4 The median has at least one advantage over the mean in that
a) it is not much affected by extreme scores.
b) it is easier to calculate than the mode.
c) it is usually closer to the population mean than the mode.
d) it varies less from sample to sample.
Q:
3+ If we were interested in studying salaries in the National Basketball Association, the least useful measure of the typical salary would be
a) the median.
b) the mode.
c) the range.
d) the mean.
Q:
2+ For the following set of data [5 9 5 5 2 4], the mean is
a) 4
b) 4.5
c) 5
d) 6
Q:
1 The best measure of central tendency
a) is the mean.
b) is the median.
c) is the mode.
d) depends on the data and the question you want to ask.
Q:
17+ "5s" represents what numbers on a stem-and-leaf display according to Tukey?
a) 50-51
b) 52-53
c) 54-55
d) 56-57
Q:
16 On October 25, 1978 the Washington Post presented a graphic showing the declining purchasing power of the U.S. dollar. What was worth $1 in 1958 was worth only $0.44 in 1978. They illustrated the decline in value by showing a dollar that was 3 inches by 1 inch in 1959, and one that was 1.32 inches (44% of 3 inches) by .44 inches in 1978. What is wrong with this kind of a display?
a) You can"t equate dollars in 1958 with dollars in 1978.
b) The dollar actually increased in purchasing power over that period of time.
c) There is nothing wrong with doing this.
d) *The area of the dollar is reduced by more than .44%.
Q:
15 Inglehart (1990) presented data on the mean Satisfaction with Life scores for 24 developed countries. These data follow:Country Mean Satisfaction Country Mean SatisfactionPortugal 5.5 Canada 7.2Greece 5.8 Belgium 7.3Japan 6.4 Britain 7.5Spain 6.5 U.S.A. 7.55Italy 6.5 Ireland 7.7South Africa 6.6 Luxemburg 7.75France 6.6 Finland 7.75Argentina 6.72 Norway 7.85Hungary 6.95 Australia 7.9Austria 7.1 Switzerland 7.95Netherlands 7.2 Denmark 8.0West Germany 7.2 Sweden 8.0A histogram of these data would bea) reasonably symmetric.b) positively skewed.c) very bimodal.d) impossible to draw.
Q:
14 The data in the previous question show a much higher incidence of low birth weight babies from mothers who smoke. This finding is likely to be a reliable one because
a) everyone knows that smoking is a bad thing.
b) the smokers rate of low birth weight is twice that of the non-smokers.
c) the pattern of differences occurs reliably over each of 5 years.
d) there is a general increase in low birth weight over the years.
Q:
13+ The Center for Disease Control has published statistics relating maternal smoking to low birth weight. The data follow in terms of the percentage of birth weights < 2500 grams for mothers in each of the two groups. 1989 1990 1991 1992 1993Smokers 11.36% 11.25 11.41 11.49 11.84NonSmokers 6.02% 6.14 6.36 6.35 6.56Which of the following ways of presenting the data would be most informative?a) a histogramb) a time series graph with a line for smokers and one for non-smokersc) two pie chartsd) a stem-and-leaf display
Q:
12 The following graphic is adapted from one in Wainer (1984), plotting the number of private and public elementary schools (in thousands) in the U.S. between 1930 and 1970. Wainer was presenting it as a bad example, and I have made it worse. What is bad about this example? a) The three dimensional effect only makes the graph harder to read.
b) Any change in the number of private schools is difficult to see.
c) The time intervals on the abscissa are too broad.
d) *a and b but not c
Q:
11 A stem-and-leaf display is often
a) a simplified representation of the underlying data.
b) a quick way to draw a histogram.
c) more informative than the corresponding histogram.
d) all of the above
Q:
10 When we plot a histogram, the values on the X axis are
a) the real lower limits and real upper limits
b) the midpoints
c) the integers closest to the boundaries.
d) any of the above, depending on what makes the most sense at the time
Q:
9+ For the data referred to in the previous question, the distribution would best be called
a) bimodal.
b) unimodal.
c) symmetric.
d) balanced.
Q:
8+ Assume that we had the following set of data:Score 11 12 17 18 19 20 21 22 23 24 25Frequency 2 1 5 8 6 12 13 10 15 9 8These data would most likely be characterized asa) positively skewed.b) normal.c) negatively skewed.d) uniformly distributed.
Q:
7 In the text there was a stem-and-leaf display showing the performance of students who attended class regularly and those who often skipped class. This display illustrated
a) that poor attendees did more poorly than good attendees.
b) the shape of the two distributions.
c) the dispersion of the two distributions.
d) all of the above
Q:
6 If you created a stem-and-leaf display of the math SAT scores of all entering students in a large Midwestern state university, the leaves would most likely be
a) the numbers 2 through 8.
b) the numbers 0 through 9 (with code |6|5 = 650).
c) t, f, c.
d) the symbols * and .
Q:
5+ If you created a stem-and-leaf display of the math SAT scores of all entering students in a large Midwestern state university, the stem would best be
a) the numbers 0 through 10.
b) the numbers 200 through 800.
c) the numbers 2 through 8.
d) it is impossible to tell
Q:
4+ Outliers are
a) extreme or unusual values.
b) the lowest value in a data set.
c) the lowest and highest scores in a data set.
d) all of the above
Q:
3 The "real lower limit" of an interval in a histogram is
a) the lowest integer value for scores in that interval.
b) the midpoint of the interval.
c) the lowest continuous value that would be rounded up into that interval.
d) the smallest width of the interval.
Q:
2+ Assume that you have a set of data with 70 values spread fairly evenly between 0 and 100. The optimal number of categories for a histogram of these data would be approximately
a) 4
b) 10
c) 25
d) 50
Q:
1 Frequency distributions are used
a) as a first step in examining data.
b) as a screening device to identify questionable values.
c) to organize data.
d) all of the above
Q:
57 Use two terms to describe the following data.