Deck 3: Summarizing Data: Central Tendency

Question 1

Which of the following is not a symbol used with samples?

A) x
B) M
C) $\mu$
D) n

Answer 1

$\mu$

Question 2

A researcher records the following data for the number of dreams recalled during a night of sleep for 10 college students: 3,2,4,4,3,1,1,0,2,and 0.Is the mean equal to the median in this example?

A) Yes.
B) No; the median is larger than the mean.
C) No; the mean is larger than the median.
D) There is not enough information to answer this question.

Answer 2

Yes.

Question 3

A researcher reports that "the average shopper in the sample (n = 12)purchased $65.00 worth of items ( $\mu$ = $65.00)during a busy shopping day." What mistake was made in this citation?

A) None; this citation is written appropriately.
B) The sample mean is written using the wrong notation.
C) The sample size is written using the wrong notation.
D) Both the sample mean is written using the wrong notation and the sample size is written using the wrong notation.

Answer 3

The sample mean is written using the wrong notation.

Question 4

A researcher records the following data for the number of complaints filed (per day)following a controversial policy change at a local business: 3,8,5,0,4,6,2,1,1,4,2,and 0.Is the mean equal to the median in this example?

A) Yes.
B) No; the median is larger than the mean.
C) No; the mean is larger than the median.
D) There is not enough information to answer this question.

Question 5

The ______ is the sum of all scores (in a sample or population)divided by the number of scores summed.

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

Question 6

A researcher records the following data for the time (in seconds)it takes five rats to cross an electrical grid to obtain reinforcement on the other side: 12,9,13,4,and 12.Is the mean equal to the mode in this example?

A) Yes.
B) No; the mode is larger than the mean.
C) No; the mean is larger than the mode.
D) There is not enough information to answer this question.

Question 7

A staff member records the number of victories (per 10-game season)for a new football coach during his first three seasons with a team.The coach won 1,3,and 8 games,respectively,over the three seasons.Which conclusion is appropriate?

A) The football coach won an average of four games per season.
B) The football coach won a median of three games per season.
C) The football coach won 40% of his games during his first three seasons.
D) All of these.

Question 8

When would it be appropriate to calculate a population mean?

A) When data are measured for a portion of individuals from a population.
B) When the sample mean is not available.
C) When data are measured for all members of a population.
D) When it is not possible to measure all data in a population.

Question 9

Which type of mean is used to describe a portion of individuals in a given population?

A) sample mean
B) population mean
C) restricted mean
D) none of these

Question 10

A researcher reports "the average patron (n = 22)in a local bar consumed more than twice the number of drinks (per day)on weekends (M = 5.4 drinks)compared to weekdays (M = 2.3 drinks)." Although not stated directly,how do we know that the patrons in this study constitute a sample and not a population of patrons at this local bar?

A) We can't know for sure because this was not stated directly.
B) The notation for a sample mean was used.
C) The notation for a sample size was used.
D) Both the notation for a sample mean was used and the notation for a sample size was used.

Question 11

The ______ is the value that occurs most often or at the highest frequency in a distribution.

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

Question 12

A researcher records the following data for the number of different food items chosen by seven participants in a buffet-style setting: 1,6,2,5,4,3,and 7.Is the mean equal to the median in this example?

A) Yes.
B) No; the median is larger than the mean.
C) No; the mean is larger than the median.
D) There is not enough information to answer this question.

Question 13

The ______ is the middle value in a distribution of scores that are listed in numeric order.

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

Question 14

The mathematical term is the numerator for

A) the population mean.
B) the sample mean.
C) both the population mean and the sample mean.
D) none of these; this term is not in the numerator for any calculation.

Question 15

The size of a population is symbolized as ______,whereas the size of a sample is symbolized as ______.

A) $\mu$ ; M
B) M; $\mu$
C) n; N
D) N; n

Question 16

The population mean is symbolized as ______,whereas the sample mean is symbolized as ______.

A) $\mu$ ; M
B) M; $\mu$
C) n; N
D) N; n

Question 17

What terms refer to the meaning of each of the following measures,respectively: mean,median,and mode?

A) middle, most, and average
B) average, middle, and most
C) average, most, and middle
D) most, average, and middle

Question 18

Given the same set of data for a population and sample,would the mean for both data sets be equal?

A) No, the population mean would be larger.
B) No, the sample mean would be larger.
C) Yes, but only if the sample size equaled the population size.
D) Yes, this would be true anytime both data sets are the same.

Question 19

Which of the following can be used to estimate the median?

A) the 50th percentile of a relative percentage distribution
B) the 50th percentile of a cumulative percentage distribution
C) the mean
D) the mode

Question 20

If a portion of people from a population are asked to complete an assessment,then the average score among that group of people would be considered a

A) sample mean.
B) population mean.
C) median split.
D) modal mean.

Question 21

The ______ is an arithmetic mean of a weighted or disproportionate set of scores.

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

Question 22

A researcher selects a sample of 6 men and 11 women.She asks participants to rate the likelihood they would do female-stereotyped jobs (such as nursing or school teaching)on a scale from 1 = not likely at all to 5 = very likely.Men indicated that they would be less likely to do these jobs (M = 2.1)compared with women (M = 4.3).What is the weighted mean for the combined sample of 17 total participants?

A) 2.1
B) 4.3
C) 3.2
D) 3.5

Question 23

The sum of the squared differences of scores from their mean is

A) minimal.
B) zero.
C) negative.
D) negligible.

Question 24

A researcher selects a sample of six professors,six students,and six administrators at a local school and has them rate the effectiveness of an innovative new teaching style.In this example,is it possible that the weighted mean ratings will equal the arithmetic mean for the entire sample of 18 participants?

A) No, the weighted mean is never exactly equal to the arithmetic mean.
B) Yes, because there are an equal number of participants in each sample.
C) Yes, because the sample sizes are selected from the same school.
D) It is not possible to know this without knowing the mean for each sample.

Question 25

To measure attraction,a researcher records the following data for the distance (in inches)between two persons sitting in a waiting room: 46,32,10,23,18,46,and 60.Is the mode equal to the median in this example?

A) Yes.
B) No; the median is larger than the mode.
C) No; the mode is larger than the median.
D) There is not enough information to answer this question.

Question 26

The fact that the sum of the differences of scores from their mean is zero best illustrates that

A) the mean is at the center of a distribution.
B) the mean is the "balance point" of a distribution.
C) the mean is equal to zero.
D) the mean can never be negative.

Question 27

Which of the following will decrease the value of the mean?

A) deleting a score below the mean
B) adding a score below the mean
C) adding a score exactly equal to the mean
D) none of these

Question 28

Which of the following is NOT a characteristic of the mean?

A) Add a score above the mean and the mean will increase.
B) Add a score below the mean and the mean will decrease.
C) Delete a score below the mean and the mean will increase.
D) Delete a score above the mean and the mean will increase.

Question 29

Multiplying or dividing each score in a distribution by the same constant will

A) cause the mean to change by that constant.
B) not change the mean at all because each score is multiplied or divided by the same constant.

Question 30

Adding the same constant to each score in a distribution (or subtracting the same constant from it)will

A) cause the mean to change by that constant.
B) not change the mean at all because the same constant is added to or subtracted from each score.

Question 31

Which of the following statements about a weighted mean is true?

A) The weighted mean is always equal to the arithmetic mean.
B) The weighted mean can only be reported if the sample size is equal in each group.
C) The weighted mean is used to compute the combined mean for two or more samples of scores in which the number of scores in each sample is disproportionate or unequal.
D) The weighted mean is heavier than an arithmetic mean.

Question 32

A researcher records the following data for how participants rated the likability (on a scale from 1 = not liked at all to 7 = very likable)of an individual who blushed after making a mistake: 5,4,7,6,6,4,6,7,2,5,and 6.Is the mode equal to the median in this example?

A) Yes.
B) No; the median is larger than the mode.
C) No; the mode is larger than the median.
D) There is not enough information to answer this question.

Question 33

A researcher records the following scores: 5,3,7,6,2,8,0,and 1.In terms of these data,the sum of the squared differences of scores from their mean is ______.

A) 0
B) 8
C) 60
D) 164

Question 34

A researcher records the following data for the number of times an interviewer is interrupted during a series of interviews: 0,0,3,2,5,3,0,8,0,2,1,and 1.Is the mode equal to the median in this example?

A) Yes.
B) No; the median is larger than the mode.
C) No; the mode is larger than the median.
D) There is not enough information to answer this question.

Question 35

A researcher records 52 scores.What is the median position of these scores?

A) the 26th score in numeric order
B) the average of the 26th and 27th scores in numeric order
C) the 27th score in numeric order
D) it's not possible to know this without the raw scores

Question 36

A researcher asks participants to estimate the height (in inches)of a statue that is in a waiting area.The researcher records the following estimates: 40,46,30,50,and 34.If the researcher removes the estimate of 40 (say,due to an experimenter error),then the value of the mean will

A) decrease.
B) increase.
C) remain the same.
D) become negative.

Question 37

A professor grades 120 research papers and reports that the average score was 80%.What do we know about the sum of the differences of these 120 scores from their mean of 80%?

A) The sum of the differences is minimal.
B) The sum of the differences is 80%, the same as the mean.
C) The sum of the differences is equal to zero.
D) It is impossible to know without knowing each of the 120 scores.

Question 38

A researcher records 17 scores.What is the median position of these scores?

A) the 9th score in numeric order
B) the average of the 9th and 10th scores in numeric order
C) the average of the 8th and 9th scores in numeric order
D) it's not possible to know this without the raw scores

Question 39

A researcher measures the mean time (in seconds)it takes two groups of children to complete an activity task.She finds that Group A (M = 22 s)completed the task more quickly than Group B (M = 36 s).She then computes a weighted mean for both groups combined and calculates a weighted mean equal to 26.Based on the information provided,which group had a larger sample size?

A) Group A.
B) Group B.
C) The sample size is equal in both groups.
D) It is not possible to know this without knowing the sample size for each group.

Question 40

A researcher asks participants to estimate the calories they consume in a meal.The researcher records the following estimates: 450,426,310,500,and 220.If the researcher removes the estimate of 220 (perhaps because the participant drops out of the study),then the value of the mean will

A) decrease.
B) increase.
C) remain the same.
D) become negative.

Question 41

A researcher asks adult participants to rank their top five favorite songs from their childhood.Based on the scale of measurement described,which measure of central tendency is most appropriate to describe these data?

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

Question 42

The mean would be used to describe which of the following variables?

A) rankings
B) distance traveled in miles
C) gender
D) model of car

Question 43

The mean is the balance point for a distribution.

Question 44

The sample mean is symbolized as M; the population mean is symbolized as $\mu$ .

Question 45

The numerator of the sample mean and the population mean is the same.

Question 46

Three measures of central tendency are the mean,median,and range.

Question 47

The formulas for a population mean and a sample mean are defined using the same notation.

Question 48

The sample size is in the denominator of the calculation of a sample mean.

Question 49

The population mean is used to estimate the value of a sample mean.

Question 50

The median would be used to describe which of the following variables?

A) gender
B) ethnicity
C) rankings
D) brand name

Question 51

Although the mean is a measure of central tendency,it is not always located exactly at the center of a distribution.

Question 52

The median is an appropriate measure of central tendency for

A) data that are positively skewed.
B) data that are negatively skewed.
C) data that are on an ordinal scale.
D) all of these.

Question 53

The mean is an appropriate measure of central tendency for

A) data that are normally distributed.
B) data that are on an interval or ratio scale.
C) data in which the mean, median, and mode are equal.
D) all of these.

Question 54

The median is the balance point for a distribution.

Question 55

The mode can be used with the mean to describe which of the following variables?

A) rankings
B) gender
C) the winning percentage of teams in a league
D) all of these

Question 56

The mode is an appropriate measure of central tendency for

A) data that are bimodal.
B) use with other measures of central tendency.
C) data that are on a nominal scale.
D) all of these.

Question 57

A researcher records the time (in seconds)that participants arrive late for a scheduled research study.Assuming these data are normally distributed,which measure of central tendency is most appropriate to describe these data?

A) mean
B) median
C) mode
D) None; it is inappropriate to describe the central tendency of these data.

Question 58

The formulas for a population and sample mean only differ by notation; otherwise,these formulas are calculated in the same manner.

Question 59

A researcher records the hospital admission rates for coronary heart disease at 10 local hospitals.She finds that two different hospitals had the highest overall rates of hospital admissions.Which measure of central tendency did this researcher use to describe these data?

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

Question 60

The distribution of annual household income in the United States is positively skewed.If the median annual income is about $56,000,this implies that the mean annual household income in the Unites States is

A) smaller.
B) larger.
C) the same.
D) There is not enough information to answer this question.

Question 61

A skewed distribution tends to pull the median,but not the mean,toward outliers in the data.

Question 62

The mode is always the middle score in a distribution.

Question 63

The weighted mean is used to determine the mean for samples with unequal sample sizes.

Question 64

A researcher measures the following scores on an assessment: 2,3,7,3,5,6,and 9.In this example,the mean is smaller than the median.

Question 65

A weighted mean should be used when the "weights" are not equal.

Question 66

Adding a new score to a set of scores will change the mean,even when the score that is added is equal to the mean.

Question 67

The mode and the median are always the same value.

Question 68

A researcher measures the depth (in fathoms)of different points in the ocean affected most by pollution.Based on the scale of measurement for these data,describing the mean depth is appropriate.

Question 69

A weighted mean weighs the mean by the sample size for each sample in the formula.

Question 70

A weighted mean is most appropriate to describe the mean for two or more samples with equal sample sizes.

Question 71

Some,but not all,scores in a distribution are included in the calculation of a mean.

Question 72

The median cannot be at the center of a distribution if the mean is also at the center of the distribution.

Question 73

The mean,median,and mode are all the same value in a normal distribution.

Question 74

It is appropriate to use the mode with the mean to describe data that are skewed.

Question 75

The mode can be used to describe modal distributions.

Question 76

The sum of the squared differences of scores from their mean is zero.

Question 77

The sum of the differences of scores from their mean is zero.

Question 78

A researcher measures the following scores on a quiz: 0,3,7,3,5,4,and 6.In this example,the mean is larger than the median.

Question 79

A researcher records the distance (in feet)traveled in a burning building by firefighters during a rescue attempt.Based on the scale of measurement for these data,describing the mean distance traveled is appropriate.

Question 80

It is possible to compute a sample mean that is larger than the value of the actual population mean.