Deck 16: Statistical Reasoning in Everyday Life

Question 1

For which of the following distributions of scores would the median most clearly be a more appropriate measure of central tendency than the mean?

A) 16, 28, 4, 8, 24
B) 9, 6, 9, 12, 9
C) 8, 9, 12, 10, 16
D) 6, 18, 4, 5, 2

Answer 1

6, 18, 4, 5, 2

Question 2

In any distribution of scores, an equal number of scores are both greater than and less than

A) the mode.
B) the mean.
C) the median.
D) any of these measures of central tendency.

Answer 2

the median.

Question 3

To understand the British newspaper headline "Income for 62% Is Below Average," it is necessary to appreciate the distinction between the ________ and the mean.

A) range
B) standard deviation
C) mode
D) median

Answer 3

median

Question 4

The standard deviation is a measure of

A) central tendency.
B) variation.
C) statistical significance.
D) correlation.

Question 5

Variation is to central tendency as ________ is to ________.

A) range; median
B) mode; mean
C) scatterplot; bar graph
D) correlation; scatterplot

Question 6

Two students in an art class are at least 20 years older than the others. Which measure of variation of class members' ages is most affected by the ages of these two students?

A) standard deviation
B) mode
C) median
D) range

Question 7

Which of the following provides a rough indication of the degree of variation among a set of scores?

A) correlation coefficient
B) scatterplot
C) range
D) median

Question 8

Seven members of a girls' club reported the following individual earnings from their sale of raffle tickets: $5, $9, $4, $11, $6, $4, and $3. In this distribution of individual earnings, the

A) median is greater than the mean and greater than the mode.
B) median is less than the mean and less than the mode.
C) median is greater than the mean and less than the mode.
D) median is less than the mean and greater than the mode.

Question 9

The most familiar measure of central tendency is the

A) mode.
B) mean.
C) median.
D) standard deviation.

Question 10

Seven members of a 4H club reported the following individual earnings from their sale of cakes: $7, $13, $3, $5, $2, $9, and $3. In this distribution of individual earnings, the

A) mean is greater than the mode and greater than the median.
B) mean is equal to the mode and less than the median.
C) mean is greater than the mode and equal to the median.
D) mean is less than the mode and less than the median.

Question 11

In a distribution of test scores, which measure of central tendency would likely be the most affected by a couple of extremely high scores?

A) median
B) mode
C) standard deviation
D) mean

Question 12

The range is

A) the difference between the highest and lowest scores in a distribution.
B) the most commonly used measure of variation.
C) the average deviation of scores from the mean.
D) the most frequently occurring score in a distribution of scores.

Question 13

Standard deviation is to mean as ________ is to ________.

A) median; mode
B) variation; central tendency
C) scatterplot; bar graph
D) correlation; scatterplot

Question 14

The mode, median, and mean are measures of

A) central tendency.
B) variation.
C) correlation.
D) statistical significance.

Question 15

Measures of central tendency are most useful for

A) random sampling.
B) summarizing data.
C) preventing skewed distributions.
D) constructing scatterplots.

Question 16

Six different high school students spent $10, $13, $2, $12, $13, and $4, respectively, on entertainment. The mode of this group's entertainment expenditures is

A) $9.
B) $11.
C) $12.
D) $13.

Question 17

The mode, median, and mean are most likely to have different values when they

A) describe a skewed distribution.
B) are derived from a limited range of scores.
C) represent the central tendency of a random sample.
D) represent the central tendency of an entire population.

Question 18

The arithmetic average of a distribution of scores is the

A) mode.
B) median.
C) standard deviation.
D) mean.

Question 19

The mode of a distribution of scores is the

A) score exceeded by 50 percent of all the scores.
B) most frequently occurring score.
C) arithmetic average of all the scores.
D) difference between the highest and lowest scores.

Question 20

The percentage of college students whose gradepoint averages fall into various performance levels could be represented on a

A) standard deviation.
B) bar graph.
C) scatterplot.
D) correlation coefficient.

Question 21

Kiska used a scatterplot to display the relationship between college students' self-esteem and their feelings of depression. The points on the scatterplot are most likely clustered in a pattern that

A) resembles a bell-shaped curve.
B) extends from the upper left to the lower right of the plot.
C) resembles a U-shaped curve.
D) extends from the lower left to the upper right of the plot.

Question 22

If IQ scores are normally distributed, having a mean of 100 and a standard deviation of 15, approximately what percentage of people have IQ scores between 85 and 115?

A) 34
B) 50
C) 68
D) 95

Question 23

Akira dreamed that a handsome young man she had met the previous day asked her for a date. When he actually did call for a date several days later, Akira concluded that dreams accurately predict future events. Her belief best illustrates

A) a normal curve.
B) an illusory correlation.
C) a standard deviation.
D) a scatterplot.

Question 24

Professor Chang displays the relationship between the height and weight measurements of over 500 randomly selected people using a scatterplot. The points on the scatterplot are most likely clustered in a pattern that

A) resembles a U-shaped curve.
B) extends from the upper left to the lower right of the plot.
C) resembles a bell-shaped curve.
D) extends from the lower left to the upper right of the plot.

Question 25

On average, Caryl's school bus arrives on time, although sometimes it is a bit early or late. If the arrival times are distributed on a normal curve, which of the following statistics would enable Caryl to estimate the probability that her bus will arrive within 5 minutes of its scheduled arrival time on any given day?

A) median
B) mean
C) standard deviation
D) correlation coefficient

Question 26

Approximately 68 percent of the cases represented by the normal curve fall within ________ standard deviation(s) from the mean.

A) 1
B) 2
C) 3
D) 34

Question 27

Which of the following correlation coefficients expresses the strongest degree of relationship between two variables?

A) +0.10
B) -0.67
C) -0.10
D) +0.59

Question 28

Professor Woo noticed that the distribution of students' scores on her last biology test had an extremely small standard deviation. This indicates that the

A) test was given to a very small class of students.
B) test was a poor measure of the students' knowledge.
C) students generally performed very well on the test.
D) students' scores tended to be very similar to one another.

Question 29

A scatterplot graphically depicts the

A) standard deviation of a distribution of scores.
B) arithmetic average of a distribution of scores.
C) total population from which samples may be drawn.
D) degree of relationship between two variables.

Question 30

If a set of standardized test scores is normally distributed, having a mean of 75 and a standard deviation of 6, approximately 95 percent of the scores are somewhere between

A) 72 and 78.
B) 75 and 87.
C) 69 and 81.
D) 63 and 87.

Question 31

Approximately what percentage of the cases represented by the normal curve fall between -2 and +2 standard deviations from the mean?

A) 34
B) 68
C) 95
D) 100

Question 32

If IQ scores are normally distributed, having a mean of 100 and a standard deviation of 15, approximately what percentage of people have IQ scores between 55 and 145?

A) 34
B) 68
C) 95
D) 100

Question 33

Which of the following statistical measures is most helpful for indicating the extent to which people's happiness predicts the number of friends they have?

A) standard deviation
B) median
C) mean
D) correlation coefficient

Question 34

Which statistical phenomenon refers to the tendency for extraordinary or unusual events to be followed by more ordinary events?

A) the standard deviation
B) the normal curve
C) regression toward the mean
D) illusory correlation

Question 35

If the points on a scatterplot are clustered in a pattern that extends from lower left to upper right, this would suggest that the two variables depicted are

A) normally distributed.
B) positively correlated.
C) negatively correlated.
D) not correlated.

Question 36

A normal curve would be LEAST likely to characterize a large random sample of

A) body weights.
B) intelligence scores.
C) family incomes.
D) professional baseball batting averages.

Question 37

Students who score much higher on an exam than they usually do can reasonably anticipate ________ scores when they are retested?

A) very low
B) somewhat lower
C) equally high
D) even higher

Question 38

A correlation coefficient is a statistical measure of the

A) difference between the highest and lowest scores in a distribution.
B) extent to which two factors vary together.
C) statistical significance of a difference between two sample means.
D) frequency of scores at each level of some measure.

Question 39

To calculate the numerical value of the standard deviation, it would be most reasonable to first compute the value of the

A) mean.
B) mode.
C) correlation coefficient.
D) median.

Question 40

Which of the following correlations between annual income and education level would best enable you to predict annual income on the basis of level of education?

A) +0.05
B) -0.01
C) +0.10
D) +0.50

Question 41

A random sample of females was observed to exhibit a lower average level of self-esteem than a random sample of males. To assess the likelihood that this observed difference reflects a real difference in the average self-esteem of the total population of males and females, it is necessary to

A) construct a scatterplot.
B) calculate a correlation coefficient.
C) plot the distribution of self-esteem levels among all males and females.
D) conduct a test of statistical significance.

Question 42

To compare verbal intelligence at different age levels, researchers tested and retested a group of children from the time they were 2 until they reached the age of 20. The researcher were clearly using a

A) longitudinal study.
B) correlation coefficient.
C) cross-sectional study.
D) regression toward the mean.

Question 43

The ________ can be a particularly misleading indication of what is average for a ________ distribution of scores.

A) mean; skewed
B) median; skewed
C) mean; normal
D) median; normal

Question 44

Research in which the same group is tested and retested over a period of years is a

A) cross-sectional study.
B) scatterplot.
C) longitudinal study.
D) regression toward the mean.

Question 45

Ahmed has five sisters who are 3, 3, 5, 9, and 10 years of age. The number "5" represents the ________ of the sisters' ages.

A) mode
B) median
C) mean
D) range

Question 46

To test for age differences in intelligence, at the beginning of the school year a researcher gave the same mathematics test to groups of children who were 8, 10, 12, and 14 years of age. This procedure best illustrates a

A) scatterplot.
B) longitudinal study.
C) standard deviation.
D) cross-sectional study.

Question 47

The maximum height of a normal curve corresponds to the ________ of a normal distribution.

A) range
B) mean
C) standard deviation
D) statistical significance

Question 48

Statistical significance refers to whether research

A) variables are causally related.
B) participants were randomly assigned to conditions.
C) findings are due to chance variations.
D) results add support to previous findings.

Question 49

When people's symptoms of emotional distress are at their worst, whatever they do to try to alleviate the condition is likely to be followed by improvement rather than further deterioration. This is best explained in terms of

A) the standard deviation.
B) illusory correlation.
C) the "decline effect."
D) regression toward the mean.

Question 50

When interpreting the results of cross-sectional studies, it is especially important to consider the effects of ________ between generations.

A) the standard deviation
B) social-cultural differences
C) scatterplots
D) the normal curve

Question 51

After his property was vandalized by a small group of teenagers, Mr. Majka concluded that most teenagers are irresponsible and delinquent. Mr. Majka ought to be reminded that accurate generalizations depend on

A) a realization that random events may not look random.
B) an awareness of regression toward the mean.
C) the observation of representative samples.
D) the selection of samples from a skewed population.

Question 52

Faustin, a member of his college's golf team, has an opportunity to play against a nationally acclaimed professional golfer. How many holes of golf should Faustin choose to play with the professional in order to maximize his own slim chances of winning?

A) 9
B) 18
C) 27
D) 36

Question 53

Although Shien once scored 37 points during a single high school basketball game, he was subsequently unable to beat or match this record no matter how hard he tried. His experience may be at least partially explained in terms of

A) regression toward the mean.
B) the standard deviation.
C) an illusion of control.
D) illusory correlation.

Question 54

Unusual ESP subjects who defy chance when first tested nearly always lose their "psychic powers" when retested. This best illustrates

A) illusory correlation.
B) regression toward the mean.
C) the standard deviation.
D) the normal curve.

Question 55

An observed difference between two sample groups is more likely to be statistically significant if

A) the observed difference is small.
B) the sample groups are small.
C) the standard deviations of the sample groups are small.
D) both samples are drawn from the same population.

Question 56

If half the students at Quincy College have blue eyes, which of the following events is most probable?

A) In a Quincy College class consisting of 15 students, 80% or more have blue eyes.
B) In a Quincy College class consisting of 30 students, 80% or more have blue eyes.
C) In a Quincy College class consisting of 45 students, 80% or more have blue eyes.
D) All the above are equally probable.

Question 57

As the size of a sample ________, the size of the standard deviation is most likely to ________.

A) increases; increase
B) increases; decrease
C) decreases; remain the same
D) increases or decreases; remain the same

Question 58

One can most accurately estimate a population mean if a sample is

A) large in size and low in variability.
B) small in size and high in variability.
C) large in size and high in variability.
D) small in size and low in variability.

Question 59

The average scores of two samples taken from the same population are most likely to differ if

A) the samples are both small.
B) the standard deviations of the samples are both small.
C) the samples differ from each other in size.
D) the sample means are both similar to the sample medians.

Question 60

The ________ is a measure of ________.

A) median; variation
B) range; central tendency
C) standard deviation; variation
D) correlation coefficient; central tendency

Question 61

In which type of study are the same people tested and retested over a period of years?

A) cross-sectional
B) correlational
C) longitudinal
D) scatterplot

Question 62

The first step in constructing a bar graph is to

A) measure the standard deviation.
B) organize the data.
C) calculate a correlation coefficient.
D) determine the range.

Question 63

One person in a 10-person group is 10 times older than any of the other members. With respect to age, it is MOST likely that the majority of group members are younger than the group's

A) mode.
B) median.
C) mean.
D) standard deviation.

Question 64

In a normal distribution, what percentage of scores fall between -1 and +1 standard deviation units of the mean?

A) 50 percent
B) 68 percent
C) 95 percent
D) 99.7 percent

Question 65

What is the mean of the following distribution of scores: 2, 5, 8, 10, 11, 4, 6, 9, 1, 4?

A) 2
B) 10
C) 6
D) 15

Question 66

Differences between two samples are LEAST likely to be statistically significant if the samples are ________ and the standard deviations of the samples are ________.

A) small; small
B) large; large
C) small; large
D) large; small

Question 67

What is the median of the following distribution: 10, 7, 5, 11, 8, 6, 9?

A) 6
B) 7
C) 8
D) 9

Question 68

Which of the following sets of scores would likely be most representative of the population from which it was drawn?

A) a sample with a relatively large standard deviation
B) a sample with a relatively small standard deviation
C) a sample with a relatively large range
D) a sample with a relatively small range.

Question 69

Why is the median at times a better measure of central tendency than the mean?

A) It is more sensitive to extreme scores.
B) It is less sensitive to extreme scores.
C) It is based on more of the scores in the distribution than the mean.
D) It is the arithmetic average.

Question 70

The following scatterplot depicts a correlation coefficient that would be close to

A) +1.0.
B) -1.0.
C) 0.00.
D) 0.50.

Question 71

The value of the correlation coefficient indicates the ________ of relationship between two variables, and the sign (positive or negative) indicates the ________ of the relationship.

A) direction; strength
B) strength; direction
C) direction; reliability
D) reliability; strength

Question 72

Standard deviation is to mode as ________ is to ________.

A) mean; median
B) variation; central tendency
C) median; mean
D) central tendency; variation

Question 73

Which statistic is the average amount by which the scores in a distribution vary from the average?

A) standard deviation
B) range
C) median
D) mode

Question 74

What is the mode of the following distribution of scores: 2, 2, 4, 4, 4, 14?

A) 2
B) 4
C) 5
D) 6

Question 75

The most frequently occurring score in a distribution is the

A) mean.
B) median.
C) mode.
D) range.

Question 76

The precision with which sample statistics reflect population parameters is greater when the sample is

A) large.
B) characterized by high variability.
C) small in number but consists of vivid cases.
D) statistically significant.

Question 77

If a difference between two samples is NOT statistically significant, which of the following can be concluded?

A) The difference is probably not a true one.
B) The difference is probably not reliable.
C) The difference could be due to sampling variation.
D) All of these statements are true.

Question 78

Which of the following is true of the cross-sectional method?

A) It compares people of different ages with one another.
B) It studies the same group of people at different times.
C) It tends to paint too favorable a picture of the effects of aging on intelligence.
D) It is more appropriate than the longitudinal method for studying intellectual change over the life span.

Question 79

In the following distribution, the mean is ________ the mode and ________ the median: 4, 6, 1, 4, 5.

A) less than; less than
B) less than; greater than
C) equal to; equal to
D) greater than; equal to

Question 80

The ________ is a measure of ________.

A) standard deviation; central tendency
B) mean; variation
C) median; central tendency
D) mode; variation