Deck 3: Summarizing Data: Central Tendency

Question 1

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

Answer 1

$\mu$ ;M

Question 2

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 the above

Answer 2

all of the above

Question 3

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

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

Answer 3

median

Question 4

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 5

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 6

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 7

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 is 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 B and C

Question 8

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 9

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 sample size was used.
D)both B and C

Question 10

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.

Question 11

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 12

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 13

The mathematical term ∑x is the numerator for

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

Question 14

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

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

Question 15

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 16

What terms refer to 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 17

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 the above

Question 18

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 19

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 20

When would a researcher calculate a population mean?

A)when data are measured for of a portion of individuals from a population
B)when the sample mean it 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 21

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 22

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 23

A researcher selects a sample of 6 professors,6 students,and 6 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 even number of participants in each sample.
C)Yes,because the sample sizes are equal in this example.
D)It is not possible to know this without knowing the mean for each sample.

Question 24

A professor grades 120 research papers and reports that the average score was an 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 25

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 26

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 seconds)completed the task more quickly than Group B (M = 36 seconds).She then computes a weighted mean for both groups combined and calculates = 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 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 the above

Question 28

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

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

Question 29

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

A)The weighted mean is always equal to the arithmetic mean.
B)The weight mean can only be reported id 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 30

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

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

Question 31

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 32

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)32
D)60

Question 33

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 34

A researcher asks participants to estimate the height (in inches)of a statue that was 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 35

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 36

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 was multiplied or divided by the same constant

Question 37

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 38

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 was added to or subtracted from each score

Question 39

A researcher selects a sample of 6 males and 11 females.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 this entire sample of 17 participants?

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

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

The mean is the balance point for a distribution.

Question 42

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 the above

Question 43

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 44

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

A)rankings
B)gender
C)volume in a container
D)all of the above

Question 45

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

Question 46

The median is the balance point for a distribution.

Question 47

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

Question 48

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

Question 49

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

Question 50

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)range

Question 51

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 52

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

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

Question 53

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

Question 54

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

Question 55

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 the above

Question 56

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

Question 57

The distribution of personal income for U.S.citizens is positively skewed.If the median annual income is $44,000,this implies that the mean annual income is

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

Question 58

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

Question 59

A researcher records the hospital admission rates for coronary heart disease at 10 local hospitals.She finds that 2 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 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 the above

Question 61

The mode is the middle score in a distribution.

Question 62

The sample mean equal to 3.20 is equal to a population mean of 3.20.

Question 63

A weighted mean is appropriate when describing the mean for two or more samples with equal sample sizes.

Question 64

The weighted mean can be computed to determine the mean for samples with unequal sample sizes.

Question 65

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

Question 66

The mode and the median are always the same value.

Question 67

The mode can be used to describe modal distributions.

Question 68

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

Question 69

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

Question 70

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

Question 71

A weighted mean must be used when the "weights" are all equal.

Question 72

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

Question 73

Some,but not all scores in a distribution,influences the value of the mean.

Question 74

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

Question 75

The mode should be used with the mean to describe skewed distributions.

Question 76

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 77

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 78

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 79

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 80

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