Statistics Ch. 2

A stem and leaf display is a device for sorting data on the basis of a) leading and trailing digits. b) class intervals. c) relative frequency. d) degree of precision.

A

Cumulative frequencies indicate a) how many observations fall at or below a particular class. b) how many observations fall at or above a particular class. c) either a or b depending on your perspective. d) neither a nor b

A

Frequency distributions for qualitative data are relatively easy to construct because a) classes or categories are dictated by the data. b) they usually are based on small total numbers of observations. c) data patterns are more detectable. d) all of the above

A

In a frequency distribution for ungrouped data, a) class intervals are of size one. b) observations are over summarized. c) duplicate observations can't occur. d) the range of possible observations should be very large.

A

One inevitable byproduct of grouping data is the loss of a) the identities of individual observations. b) some data. c) some regularities or patterns in the data. d) all of these

A

(NOTE: This question requires display of frequency distribution in 2.13.) If this frequency distribution represents the test scores for a class of ten college students, we can infer that the test probably is a) too easy. b) too difficult. c) multiple choice. d) essay.

B

. (NOTE: This question requires display of frequency distribution in 2.13.) The relative frequency of the interval 75 89.99 equals a) 0.10 b) 0.20 c) 0.50 d) none of these

B

A valid outlier a) is to be avoided at all costs. b) might enhance your understanding. c) occurs in almost every batch of data. d) indicates poor data-collecting techniques.

B

If you wish to graph the distribution of times spent dreaming during sleep (as inferred from rapid eye movements) for a sample of young adults, use a) a histogram or bar graph. b) a histogram or frequency polygon. c) a bar graph or frequency polygon. d) any of these

B

In a well constructed frequency distribution, the size of the gap between the boundaries of classes always equals a) the width of the class. b) the unit of measurement. c) some convenient number. d) a value of one.

B

The assignment of exact percentile ranks requires a) excessive computations. b) ungrouped data. c) accurate computations. d) a large total number of observations.

B

When constructing a graph, you must first decide on the type of graph. This decision depends on a) the total number of observations. b) whether data are quantitative or qualitative. c) whether data are grouped or ungrouped. d) the impression that you wish to create.

B

For the following frequency distribution, X f 80 89 4 70 79 2 60 69 11 50 59 3 20 the interval 70 79 has an approximate percentile rank of a) 20 b) 30 c) 80 d) none of the above

C

Frequency polygons are particularly useful when a) data are qualitative. b) data are ungrouped. c) two or more frequency distributions are to be displayed on the same graph. d) the original frequency distribution is to be portrayed with complete accuracy.

C

To convert a frequency distribution into a relative frequency distribution, a) add the frequencies of all lower intervals. b) change proportions to percents. c) divide the frequency for each interval by the total frequency for the entire distribution. d) move the decimal point two places to the right.

C

A stem and leaf display is ideal for summarizing distributions when you want to a) produce an idealized distribution. b) compare quantitative and qualitative data. c) emphasize the orderliness of data. d) preserve the identities of the individual scores.

D

An important characteristic of histograms, frequency polygons, and stem and leaf displays is a) size. b) total area. c) relative area. d) shape.

D

Frequency distributions can be constructed for a) grouped data. b) ungrouped data. c) qualitative data. d) all of these

D

Identify the one optional guideline for a well constructed frequency distribution. a) All observations should be included in one, and only one, class. b) All classes (with both upper and lower boundaries) should be equal in width. c) All classes even those with zero frequencies--should be listed. d) All classes should have both boundaries.

D

In a frequency distribution for grouped data, the leftmost column consists of a) frequencies. b) all possible values. c) all observed values. d) class intervals.

D

It wouldn't make sense to determine _____________ for the frequency distribution of ethnic groups within the state of New York. a) cumulative frequencies b) cumulative relative frequencies c) percentile ranks d) any of these

D

Outliers are a) worthless observations. b) inaccurate observations. c) illegal observations. d) very extreme observations.

D

Relative frequency distributions allow us to focus on a) the part or fraction of the total frequency that occupies each class. b) the relative density of observations among different classes or categories within the same distribution. c) the shapes of two or more distributions based on different total numbers of observations. d) all of the above

D

(NOTE: This question requires display of frequency distribution in 2.13.) The approximate percentile rank for the interval 90 104.99 is a) 10 b) 70 c) 80 d) none of these

C

In the following frequency distribution, X f 6 1 5 2 4 3 3 0 2 0 1 3 10 an X value of 1 has a percentile rank of a) 4 b) 30 c) 40 d) 60

B

What's wrong with the following frequency distribution? X f 220 239 1 200 219 0 160 199 0 140 159 11 120 139 17 100 119 21 70 99 14 60 69 8 30 59 7 20 29 2 0 19 1 82 a) gaps between classes b) unequal classes c) not exactly ten classes d) nothing is wrong

B

Which one of the following isn't a frequency distribution for qualitative data? a) type of transportation used by college students b) length of marriages at time of divorce decrees c) ethnic backgrounds of college students d) political preferences of corporate executives

B

(NOTE: This question requires display of frequency distribution in 2.45.) Comparison of these two distributions would be facilitated by a) converting frequencies to relative frequencies. b) expressing the frequencies more exactly. c) expanding the Other category. d) ignoring the Other category.

A

In the following well-constructed frequency distribution, X f 135 149.99 1 120 134.99 0 105 119.99 1 90 104.99 1 75 89.99 2 60 74.99 5 10 the unit of measurement equals a) 0.01 b) 1.00 c) 13.99 d) 15.00

A

(NOTE: This question requires display of frequency distribution in 2.13.) The cumulative frequency for the interval 105 119.99 equals a) 1 b) 9 c) 10 d) none of these

B

(NOTE: This question requires display of frequency distribution in 2.40.) The data pattern for this distribution best can be described as a) balanced. b) lopsided. c) either balanced or lopsided, depending on your point of view. d) undecipherable because of the absence of regular frequencies.

B

When relative standing within a distribution assumes primary importance, as with some test scores, frequencies often are converted to a) relative frequencies. b) cumulative frequencies. c) cumulative relative frequencies. d) all of these

C

The term positively skewed implies that a) a minority of observations are located in the positive direction relative to the rest of the distribution. b) a minority of observations are positive and the majority of observations are negative. c) a majority of observations are located in the positive direction relative to the rest of the distribution. d) a majority of observations are positive and the minority of observations are negative.

A

To organize a set of observations, such as 2, 3, 0, 5, 8, 1, 3, 1, for number of children per household, you should use a frequency distribution for ungrouped data because a) the number of possible values is small. b) observations are whole numbers. c) observations tend to cluster together. d) data are quantitative.

A

Too little summarization tends to occur if the frequency distribution contains a) too many classes. b) too few classes. c) unequal classes. d) open ended classes.

A

When constructing graphs, it's considered good practice to make the vertical axis a) about as tall as the horizontal axis is wide. b) taller than the horizontal axis is wide. c) shorter than the horizontal axis is wide. d) none of the above

A

Whenever an outlier is encountered, first attempt to a) verify its accuracy. b) segregate it from any summary of data. c) relegate it to a footnote. d) study the special circumstances that produce it.

A

(NOTE: This question requires display of frequency distribution in 2.13.) The class interval width equals a) 13.99 b) 15 c) 60 d) none of these

B

(NOTE: This question requires display of frequency distribution in 2.13.) The overall appearance or shape of this distribution is a) balanced. b) lopsided. c) regular. d) impossible to determine from the information given.

B

A frequency distribution of standardized IQ scores for equal numbers of male and female grade school children probably will be a) bimodal. b) normal. c) positively skewed. d) negatively skewed.

B

A frequency polygon is a) a type of bar graph. b) a line graph. c) an appropriate graph for qualitative data. d) especially appropriate for small batches of data.

B

Adjacent bars in histograms share common boundaries in order to a) produce a more compact graph. b) present the data without artificial disruptions. c) minimize the effort involved in constructing the graph. d) comply with a widely adopted convention.

B

Bar graphs are designed for use with a) quantitative data. b) qualitative data. c) ranked data. d) ungrouped data.

B

Frequency distributions that approximate a bell shaped silhouette are described as a) bimodal. b) normal. c) positively skewed. d) negatively skewed.

B

. If you wish to use a single bar graph to compare two different frequency distributions for instance, one for alcoholics and one for non-alcoholics -- it would be essential to a) double the frequency scale. b) double the width of the horizontal axis. c) use some technique, such as shading, to distinguish between the bars for the two distributions. d)use some technique, such as the selection of axes that maximizes the differences between the two distributions.

C

.(NOTE: This question requires display of frequency distribution in 2.45.) Generally speaking, inspection of the above table suggests that a) males and females are about equally likely to commit suicide. b) females are about equally likely to use any of the four methods. c) males are much more likely to use firearms than females. d) males are much more likely to use poison than females.

C

To determine the real limits of a class interval, a) ignore gaps between intervals. b) simply find the difference between tabled boundaries. c) add the tabled boundaries and divide by two. d) locate the midpoints in gaps between tabled boundaries.

D

What's wrong with the following frequency distribution? X f 200 249 23 150 199 32 100 149 16 50 99 7 78 a) unequal classes b) gaps between classes c) exclusion of zero d) too few classes

D

Which of the following is not a property of histograms? a) Units along the vertical axis reflect frequency. b) Units along the horizontal axis reflect class intervals of frequency distributions. c) Heights of bars reflect the frequencies for the various class intervals. d) The intersection of the two axes defines the lower boundary of the bottom class interval.

D

(NOTE: This question requires display of frequency distribution in 2.40.) If you could obtain more detailed information about only one class, it probably should be a) 30 or more, because this covers the largest number of possible values. b) 30 or more, because the larger values always are more informative. c) 0 4, because this class contains the largest relative frequency. d) 0 4, because the smaller values always are more informative

C

(NOTE: This question requires display of the frequency distribution in 2.33.) In the frequency distribution, a percentile rank of 60 is paired with an X value of a) 3 b) 3.5 c) 4 d) 5

C

A frequency distribution of scores on a very difficult statistics test probably will be a) bimodal. b) normal. c) positively skewed. d) negatively skewed.

C

The feature that distinguishes bar graphs from histograms is the use of a) the vertical axis for frequency. b) bars. c) gaps between bars. d) the horizontal axis for class intervals and categories.

C

The percentile rank of an observation refers to its a) rank in the distribution. b) cumulative proportion in the distribution. c) cumulative percent in the distribution. d) cumulative frequency in the distribution.

C

An androgynous person (that is, a person without either pronounced male or female tendencies) should have a percentile rank in the vicinity of _____ on a masculinity femininity scale. a) 10 b) 30 c) 50 d) 70

C

Given the following frequency distribution, SUICIDES BY METHOD, 1992 (in hundreds) METHOD MALES FEMALES Firearms 163 24 Poison 32 22 Hanging 37 9 Other 15 6 247 61 SOURCE: Statistical Abstracts of the U.S., 1995. the number of males who commit suicide with poison equals (BE CAREFUL!) a) 32 b) 320 c) 3,200 d) 32,000

C

For a given batch of data, equally competent people might choose a) a histogram or frequency polygon. b) a histogram or bar graph. c) a frequency polygon or bar graph. d) any of the above.

A

Frequency distributions for qualitative data always can be converted into a) relative frequency distributions. b) cumulative frequency distributions. c) cumulative relative frequency distributions. d) all of these

A

Histograms and frequency polygons may be viewed as the graphic counterpart of a) frequency distributions for quantitative data. b) bar graphs. c) quantitative data. d) class intervals.

A

If the incomes of equal numbers of skilled and unskilled wage earners appear in a single distribution, the resulting frequency distribution probably will be a) bimodal. b) normal. c) positively skewed. d) negatively skewed.

A

If the smallest observation equals 743 and the class interval width is to equal 50, the boundaries of the bottom class should be a) 700 749 b) 740 789 c) 743 792 d) 750 799

A

In a stem and leaf display for annual incomes, an annual income of $8,234 might be displayed as a) a stem of 8 (thousands) and a leaf of 233. b) a stem of 4 (units) and a leaf of 823. c) a stem of 8234 and no leaf. d) none of these

A

NOTE: This question requires display of frequency distribution in 2.40.) This distribution isn't quite as informative as it could be because a) only relative frequencies are used. b) too many intervals are used. c) percents are carried only one digit to the right of the decimal point. d) observations create a peculiar lopsided or unbalanced pattern.

A

Although there are many different types of misleading graphs, the book emphasizes those produced by a) falsifying data. b) withholding data. c) unscrupulous graphic techniques. d) ignorance.

C

Among a batch of 95 observations, the smallest observation equals 300 and the largest observation equals 349. Therefore, the class interval width should equal a) 1 b) 3 c) 5 d) 10

C

When constructing a histogram for the ages of college students, it would be desirable to a) locate age a type of frequency along the vertical axis. b) construct only one frequency bar for all students over the age of 40. c) break the horizontal scale (with wiggly lines) between 0 and the bottom class interval. d) clearly show along the horizontal axis the upper and lower boundaries of every class interval

C

Which one of the following is not a guideline for a well-constructed frequency distribution? a) Select the width of the class from convenient numbers. b) Aim for approximately ten classes. c) The lower boundary of the bottom class should coincide with the smallest observation. d) All classes should have both boundaries.

C

Wiggly lines can be used to signal scale breaks, and they can appear a) along the horizontal axis. b) along the vertical axis. c) both a and b d) neither a nor b

C

(NOTE: This question requires display of frequency distribution in 2.40.) The distribution permits us to conclude that a) about one-half of all divorced couples are married for fewer than 5 years. b) a substantial majority of all divorced couples are married for fewer than 20 years. c) a very small minority of all divorced couples are married for 30 or more years. d) all of the above

D

An unscrupulous person could exaggerate frequency differences in histograms or bar graphs by a) omitting the lower end of the frequency scale. b) increasing the width of taller bars. c) making the vertical axis much taller than the width of the horizontal axis. d) all of the above

D

Automobile speeds are clocked along a remote stretch of Interstate 80. If, in fact, motorists are obeying the posted 70 miles per hour speed limit, the frequency distribution of clocked speeds probably will be a) bimodal. b) normal. c) positively skewed. d) negatively skewed.

D

For a test of math achievement, it would be preferable to attain a percentile rank of a) 1 b) 43 c) 54 d) 76

D

If you wish to graph the distribution of ethnic backgrounds for a population of alcoholics, use a a) histogram. b) frequency polygon. c) stem and leaf display. d) bar graph

D

In the following frequency distribution, LENGTH OF MARRIAGE AT DIVORCE Length (years) Percent Cum Percent 30 or more 2 100 25 29 2 98 20 24 5 96 15 19 8 91 10 14 11 83 5 9 22 72 0 4 50 50 100% SOURCE: Marriage and Divorce: 1988. Vital Statistics of the United States, Vol. III, 1996. the total number of observations is a) 100 b) 1,000 c) unknown. d) unknown, but probably quite large, given the source.

D