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Q:
49 Trimmed statistics are calculated based on the entire sample.
Q:
48 The interquartile range is the range of the middle 25% of values.
Q:
47 The variance of a sample is typically a larger value than the standard deviation.
Q:
46 Of all of the measures of variability, the standard deviation is most susceptible to distortion due to outliers.
Q:
45 The difference between the lowest to the highest score in a distribution is the range.
Q:
44 The median is a measure of variability.
Q:
43 Measures of variability refer to the dispersion of data around the mean or the center.
Q:
42 Data points at the extremes of the distribution have
a) little effect on the variance.
b) distort the usefulness of the median.
c) more effect on the variance than scores at the center of the distribution.
d) are undoubtedly incorrect.
Q:
41 The population variance is
a) an estimate of the sample variance.
b) *usually an unknown that we try to estimate.
c) calculated exactly like the sample variance.
d) a biased estimate.
Q:
40 We normally compute the variance using N " 1 in the denominator because
a) it is easier that way.
b) it leads to an unbiased estimate of the sample variance.
c) it leads to an unbiased estimate of the population variance.
d) it overestimates that population variance.
Q:
39 A boxplot is better than a statistic such as the mean when your purpose is
a) to describe the central tendency of a population.
b) to describe the variability of a population.
c) to understand what a distribution of data looks like.
d) It is only worthwhile if you care only about medians.
Q:
38 A "hinge" is another word for
a) the median.
b) a quartile.
c) the range.
d) boundary.
Q:
37 If I continue to draw observations from a population and recalculate the mean each time I add an observation, the mean will approach _______ as the sample size increases.
a) its expected value
b) the true population mean
c) the median of the population if the population is symmetric
d) all of the above
Q:
36 Given the numbers 1, 2, and 3, the standard deviation is
a) 0
b) 1
c) 0.667
d) the square of the variance
Q:
35+ The disadvantage of using an interquartile range is that
a) it discards too much of the data.
b) it removes outliers only extremely high in value.
c) the positive and negative deviations balance out.
d) it is disproportionately influenced by outliers.
Q:
34 Errors that can lead to outliers can occur in
a) measurement.
b) data recording.
c) data entry.
d) all of the above
Q:
33 If the average adult male in the United States is 5" 9" tall, and the standard deviation for height is 2", approximately how many adult males would you expect to be between 5" 7" and 5"11" tall?
a) 50% of them
b) 66.7% of them
c) 75% of them
d) 90% of them
Q:
32+ The interquartile range
a) is the 50th percentile score in a data set.
b) contains as few as 25% of scores or as many as 75% of scores in a data set
c) *contains the middle 50% of scores in a data set.
d) is the same as the range.
Q:
31 The US Census Bureau collected data on family composition and found that samples from different parts of the country gave very different results for the mean number of family members living in households. If all of the data were combined to one data set,
a) the standard deviation of number of family members would probably be very small.
b) the standard deviation of number of family members would probably be relatively high.
c) the interquartile range would be small.
d) the median would equal the mean.
Q:
30 The equation is used to calculate the
a) median.
b) hinge location.
c) outer fence.
d) inner fences.
Q:
29+ A data set of intelligence scores was collected from high school seniors. The IQ scores ranged from 82 to 113. Which of the following is probably NOT a reasonable estimate of the standard deviation?
a) 6.2
b) 4.7
c) 35.4
d) All of the above are reasonable estimates.
Q:
28 The problem with measuring dispersion by merely averaging all the deviations between each score and the overall mean is that
a) positive and negative deviations will balance out.
b) squared values make intuitive interpretation difficult.
c) dividing by (N-1) gives a biased statistic.
d) There are no problems with measuring dispersion this way.
Q:
27+ Which of the following is NOT a method of describing data that reduces the role of outliers on the measurement of a data set's variability?
a) interquartile range
b) boxplot
c) range
d) trimmed statistics
Q:
26 The range is
a) the difference between the inner fences.
b) the H-spread.
c) not influenced very much by outliers.
d) the difference between the highest and lowest score.
Q:
25+ You would obtain a negative value for the variance if
a) all observations were at the mean.
b) the distribution is very negatively skewed.
c) the distribution if positively skewed.
d) you would never obtain a negative variance.
Q:
24 If we know that a set of test scores has a mean of 75 and a standard deviation of 8, we would conclude that
a) the average deviation from the mean is about 8 points.
b) the average person will have a score of 75 + 8 = 83.
c) more people are above 75 than below it.
d) You can"t tell anything about how scores lie relative to the mean.
Q:
23+ The standard deviation for the numbers 8, 9, and 10 is
a) -3.0
b) 0.0
c) .67
d) 1.0
Q:
22 The university counseling center has treated a large number of students for depression. They find that the standard deviation of depression scores for their pool of students is substantially higher after treatment than before treatment. The most likely explanation is
a) some students improved more than others.
b) some students improved substantially while others actually got worse.
c) depression therapy at the counseling center affects different students differently.
d) all of the above
Q:
21 As you increase the number of observations in a sample from 50 to 500, you are most likely to
a) leave the mean and standard deviation approximately unchanged.
b) increase the variability as the sample size increases.
c) decrease the variability as the sample size increases.
d) make the shape of the distribution more skewed.
Q:
20 If we multiply a set of data by a constant, such as converting feet to inches, we will
a) leave the mean and variance unaffected.
b) multiply the mean and the standard deviation by the constant.
c) multiply the mean by the constant but leave the standard deviation unchanged.
d) leave the mean unchanged but alter the standard deviation.
Q:
19+ Which of the following sets of data is likely to have the smallest standard deviation?
a) the distribution of SAT scores for students from your high school
b) the distribution of heights of students in an elementary school
c) the grade point averages of students from your high school's honors biology class
d) the amount that you and your friends pay for college tuition
Q:
18+ People in the stock market refer to a measure called the "standard deviation," although it is calculated somewhat differently from the one discussed here. It is a good guess that this measure refers toa) the riskiness of the stock.b) the value of the stock.c) how much the stock price is likely to fluctuate.d) how much money you are likely to earn from buying that stock.
Q:
17+ If the whiskers on a boxplot are much longer on the right than on the left, we would suspect that the distribution is
a) positively skewed.
b) negatively skewed.
c) symmetric.
d) distorted.
Q:
16 Data points that lie outside the whiskers in a boxplot are often referred to as
a) incorrect values.
b) outliers.
c) representative values.
d) deviates.
Q:
15+ Data points at the extremes of the distribution have
a) little effect on the variance.
b) more effect on the variance than scores at the center of the distribution.
c) are undoubtedly incorrect.
d) distort the usefulness of the median.
Q:
14 The whiskers in a boxplot
a) always enclose all of the data points.
b) always run from the smaller inner fence to the larger inner fence.
c) encompass the H-spread only.
d) contain all data points outside the box except the outliers.
Q:
13 In a boxplot the width of the box encompasses
a) all of the observed values.
b) all but the most extreme values.
c) approximately 50% of the observed values.
d) the center-most 10% of the values.
Q:
12 The vertical line in the center of a box plot
a) represents the sample mean.
b) represents the sample median.
c) serves to anchor the box.
d) can represent anything you want it to.
Q:
11 The difference between s and ï³ is that ï³ is
a) the value of the standard deviation in a sample.
b) the long range average of the variance over repeated sampling.
c) the biased estimate of s.
d) the value of the standard deviation in a population.
Q:
10 What do we mean by an unbiased statistic?
a) a statistic that equals the sample mean
b) a statistic whose average is very stable from sample to sample
c) a statistic used to measure racial diversity
d) a statistic whose long range average is equal to the parameter it estimates
Q:
9 The variance can best be thought of as the
a) average of the squared deviations from the mean.
b) average of the absolute deviations from the mean.
c) average of the deviations from the median.
d) square of the mean.
Q:
8+ When calculating the standard deviation we divide by N-1 rather than N because the result is
a) smaller.
b) less biased.
c) easier to interpret.
d) equal to the population mean.
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.