# Quiz 3: Measures of Central Tendency and Variability

Psychology

Q 1Q 1

The term "central tendency" refers to _____.
A)an average
B)a score around which other scores tend to cluster
C)both a and b
D)neither a nor b

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Multiple Choice

C

Q 2Q 2

_____ refers to the "average" score in a set of scores.
A)central tendency
B)variability
C)average deviation
D)none of these

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Multiple Choice

A

Q 3Q 3

Measures of _____ indicate the extent to which scores within a set differ from one another.
A)central tendency
B)variability
C)differential tendency
D)none of these

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Multiple Choice

B

Q 4Q 4

The mode of a distribution of scores:
A)is the most easily computed index of central tendency
B)is simply the score that occurs most frequently
C)has the highest "peak" in a graph of a distribution of scores
D)all of these

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Multiple Choice

Q 5Q 5

The major problem with the mode as a measure of central tendency is that:
A)there can be only one modal score
B)there can be more than one modal score
C)the mode is insensitive to variability
D)the mode is insensitive to kurtosis

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Multiple Choice

Q 6Q 6

Which of the following statements is true of the mode of any set of scores?
A)It is the score which occurs most frequently.
B)It is always less than the mean.
C)Both a and b.
D)Neither a nor b.

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Multiple Choice

Q 7Q 7

Consider the following scores achieved by subjects taking a standard IQ test: 68,83,93,100,101,103,106,120.The mode is ______.
A)93
B)101
C)97.88
D)none of these

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Multiple Choice

Q 8Q 8

If you were to randomly select one score from a set of scores,the score most likely to be selected _______.
A)would be equal to the medium of the set of scores
B)would be equal to the mode of the set of scores
C)would be equal to the mean of the set of scores
D)can vary with the numerical values of the individual scores

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Multiple Choice

Q 9Q 9

Compute the median of the following set of scores: 106,106,109,110,113,121,121.
A)109.5
B)110
C)106 and 121
D)cannot be determined from information given

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Multiple Choice

Q 10Q 10

Eight psychology students took a well-known I.Q.test and achieved the following scores: 96,98,108,110,115,120,121,142.The median score for these students is _____.
A)96
B)112.5
C)113.5
D)115

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Multiple Choice

Q 11Q 11

Which of the following statements is true of a median score?
A)It divides a distribution in half.
B)It may not have been a score actually achieved.
C)Both a and b.
D)Neither a nor b.

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Multiple Choice

Q 12Q 12

Suppose a researcher was interested in determining the effect of an experimental drug on the lifespan of laboratory rats.Shown below is a summary of the lifespans,in months,for laboratory animals administered the drug.Compute the median number of months the animals survived.
A)3.1
B)25
C)3.0
D)2.9

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Multiple Choice

Q 13Q 13

The _____ is the point in the distribution of scores that divides the distribution into two equal parts.
A)mean
B)mode
C)median
D)standard deviation

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Multiple Choice

Q 14Q 14

When there is an even number of scores,the median is the _____.
A)most frequently occurring score
B)arithmetic average of the scores
C)arithmetic average of the two middle scores
D)arithmetic average of the two most extreme scores

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Multiple Choice

Q 15Q 15

As a measure of central tendency,the median _____ the absolute difference between it and the scores in the distribution.
A)minimizes
B)maximizes
C)summarizes
D)none of these

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Q 16Q 16

The _____ is simply the arithmetic average of a set of scores.
A)median
B)mean
C)mode
D)standard deviation

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Multiple Choice

Q 17Q 17

The mean is computed by summing all of the scores and then dividing the sum by the:
A)standard deviation
B)mean divisor
C)total number of scores
D)average number of scores

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Multiple Choice

Q 18Q 18

The sum of signed deviations about the mean will always equal _____.
A)10
B)-10
C)the sum of squares
D)0

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Multiple Choice

Q 19Q 19

Most of the inferential statistics used by behavioral scientists make use of the _____ as a measure of central tendency.
A)mean
B)median
C)mode
D)all are used with equal frequency

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Multiple Choice

Q 20Q 20

The mean,median,and mode are applicable to:
A)continuous variables only
B)discrete variables only
C)continuous and discrete variables
D)interval and ratio level variables only

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Multiple Choice

Q 21Q 21

The mean of a set of scores is best described as _____.
A)a simple arithmetic average
B)an arithmetic average weighted by the number of subjects
C)usually equal to the mode
D)relatively free of the effects of extreme values

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Multiple Choice

Q 22Q 22

A teacher wants to determine the mean score of students taking a newly developed test.Her students scored as follows: 40,45,60,65,70,70,70,80,90,100.Compute the mean for the class.
A)69
B)70
C)69.5
D)none of these

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Multiple Choice

Q 23Q 23

If a researcher were to subtract the mean of a distribution from each score in that distribution and add the differences,the resulting value would _____.
A)be equal to the median
B)always be zero
C)be greater than the mode
D)depend upon the scores that make up the distribution

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Multiple Choice

Q 24Q 24

If you subtract the mean from each score in a distribution,you would obtain a set of _____.
A)signed deviation scores
B)standard individual deviation scores
C)absolute deviation scores
D)signed discrepancy scores

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Q 25Q 25

The median _____ the sum of the _____ deviations.
A)minimizes;signed
B)minimizes;unsigned
C)maximizes;signed
D)maximizes;unsigned

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Multiple Choice

Q 26Q 26

After giving a test to all members of his college class,a professor found that the scores totaled 1500 and the mean was 75.How many students took the test?
A)25
B)20
C)22
D)cannot be determined without additional information

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Multiple Choice

Q 27Q 27

In a normal distribution,the _____.
A)mean is usually higher than the mode
B)median is usually lower than the mean
C)mean,median,and mode might be equal
D)mean,median,and mode are always equal

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Multiple Choice

Q 28Q 28

The _____ is the measure of central tendency that is most sensitive to extreme values in a distribution.
A)mode
B)standard deviation
C)median
D)mean

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Multiple Choice

Q 29Q 29

The extent to which scores in a distribution differ is indicated by _____.
A)measures of central tendency
B)measures of variability
C)the result of subtracting each score from the median
D)the average of the mean and the standard deviation

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Multiple Choice

Q 31Q 31

The _____ is the highest score minus the lowest score.
A)variance
B)standard deviation
C)interquartile range
D)range

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Q 32Q 32

The _____ is the difference between the highest and lowest scores after the top 25% of the scores and the bottom 25% of the scores have been eliminated from the data.
A)range
B)interquartile range
C)intermediate range
D)intertertial range

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Multiple Choice

Q 33Q 33

The interquartile range has been criticized because it does not take into account:
A)the sum of squares
B)all of the scores in the distribution
C)none of these

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Multiple Choice

Q 34Q 34

Compute the sum of squares for the following data set: 2,2,3,6,9,13,14.
A)156
B)22.28
C)7
D)none of these

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Multiple Choice

Q 35Q 35

SS is the _____.
A)sum of standard scores
B)sum of squared deviations from the mean
C)sum of standard deviations from the mean
D)sum of standard deviations from the median

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Multiple Choice

Q 36Q 36

If SS for 30 students is 900,what is the variance?
A)5.47
B)more than 30
C)less than 30
D)exactly 30

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Multiple Choice

Q 37Q 37

The positive square root of the variance is the _____.
A)root square mean
B)standard deviation
C)variance square root
D)absolute squared deviation

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Multiple Choice

Q 39Q 39

Distributions of scores can have _____.
A)identical standard deviations with different means
B)identical means with different standard deviations
C)either a or b
D)neither a nor b

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Multiple Choice

Q 40Q 40

The sum of squared deviations from the _____ will always be _____ the sum of squared deviations around any other value.
A)median;less than
B)mode;equal to
C)mean;greater than
D)mean;less than

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Multiple Choice

Q 41Q 41

One problem with the sum of squares as an index of variability is that its size depends not only on the amount of _____ among the scores,but also on the _____ of scores.
A)variability;number
B)skewness;kurtosis
C)error;number
D)none of these

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Multiple Choice

Q 42Q 42

The variance is the:
A)sum of squares divided by N
B)the average squared deviation from the mean
C)a and b
D)neither a nor b

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Q 43Q 43

The standard deviation is the:
A)square root of the sum of squares
B)positive square root of the variance
C)negative square root of the variance
D)sum of squares divided by N

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Multiple Choice

Q 44Q 44

The best answer to the question,"What value indicates a large standard deviation?" is:
A)any value greater than 10.00
B)any value greater than 100.00
C)it depends on the variability
D)it depends on what is being measured

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Multiple Choice

Q 45Q 45

Distributions of scores can have:
A)identical variabilities but very different central tendencies
B)identical central tendencies but very different variabilities
C)a and b
D)neither a nor b

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Q 46Q 46

In positively skewed distributions,most scores occur _____ the mean and only a relatively few extreme scores occur _____ it.
A)below;above
B)at;above
C)below;above
D)at;below

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Q 47Q 47

The mean of a _____ skewed distribution will always be _____ than the median.
A)positively;less
B)negatively;less
C)negatively;greater
D)normal;less

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Multiple Choice

Q 48Q 48

If a distribution is less peaked than another,it is said to be more _____;if it is more peaked than another,it is said to be more_____.
A)skewed;variable
B)leptokurtic;variable
C)platykurtic;leptokurtic
D)leptokurtic;platykurtic

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Multiple Choice

Q 49Q 49

_____ refer(s)to the tendency for scores to cluster on one side of the mean in some distributions.
A)Unbalancing
B)Skewness
C)Both a and b
D)Neither a nor b

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Multiple Choice

Q 50Q 50

Use of Greek notation implies that the parameters describe ____ characteristics.
A)sample
B)normally distributed
C)random
D)population

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Multiple Choice

Q 51Q 51

When presenting measures of central tendency and variability,most researchers report _____ and_____ ,which are the most _____ descriptive statistics.
A)means;standard deviations;frequently used
B)means;standard deviations;precisely defined
C)means;standard deviations;generally accurate
D)none of these

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Multiple Choice

Q 52Q 52

Based on the Method of Presentation section of Chapter 3,which of the following symbols should be used to report the mean in a behavioral science journal,according to the American Psychological Association (APA)?
A)M
B)m
C)

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Multiple Choice

Q 53Q 53

Based on the Method of Presentation section of Chapter 3,the symbol n indicates
A)the sample size in a particular group.
B)the total sample size in the study.
C)the population sample size.
D)the number of groups in the study.

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Q 54Q 54

Measures of central tendency are measures of
A)deviations.
B)location.
C)distance.
D)extremes.

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Q 55Q 55

The mode is the most appropriate measure of central tendency when the scale of measurement used is
A)nominal.
B)ordinal.
C)interval.

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Multiple Choice

Q 56Q 56

Which of the following sets of data is bimodal?
A)75,85,95,105,105,105,115,125,135,135,135,145,155
B)53,62,71,80,80,80,94,99,100,132,132,145
C)2,2,2,3,3,3,3,4,5,6,7,7,7,8,8
D)20,30,30,30,30,40,50,60,70,90,100,100,100,112

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Multiple Choice

Q 57Q 57

When there is an odd number of scores,the median
A)is the arithmetic average of the middle two scores.
B)is the middle score.
C)occurs within the real limits of the middle score(s)when there are duplications of the middle score(s).
D)both a and c
E)both b and c

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Multiple Choice

Q 58Q 58

The mean is
A)the most frequently occurring score.
B)the mathematical average.
C)the midpoint of the distribution.

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Multiple Choice

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Q 60Q 60

How would you describe the relationship between the mean,median,and the mode in a positively skewed distribution?
A)mean > median > mode
B)mean < median < mode
C)mean = median = mode
D)mean > mode > median

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Multiple Choice

Q 61Q 61

Because discrete variables are only measured with whole numbers,fractions are never included when reporting the means for discrete variables.

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True False

Q 62Q 62

The range indicates the
A)average distance from the median.
B)distance between the highest and lowest scores.
C)average variability among all of the scores.

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Multiple Choice

Q 63Q 63

The interquartile range is sometimes preferred over the range because it
A)does not involve the median.
B)takes the most extreme scores into account.
C)is not based on the most extreme scores.
D)does not take into account all of the scores in a distribution.

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Multiple Choice

Q 64Q 64

If you subtract the mean from each X score and sum these scores,the sum will equal:
A)1
B)a number greater than 1
C)0
D)cannot be determined from the information given

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Multiple Choice

Q 65Q 65

One problem with the sum of squares as a measure of variability is that its size depends on _____,as well as the variability among scores.
A)the total N
B)extreme scores
C)the mode
D)the standard deviation

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Multiple Choice

Q 66Q 66

The variance is the
A)average of the deviations from the mean divided by N.
B)average of the squared deviations from the mean.
C)sum of the deviations from the mean divided by N.
D)sum of the squared deviations from the mean.

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Multiple Choice

Q 67Q 67

The standard deviation is the most easily interpreted measure of variability because it
A)does not include extreme scores.
B)is measured in square units.
C)is in the original unit of measurement.
D)is usually a number larger than the variance.

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Multiple Choice

Q 68Q 68

When comparing two different distributions,which of the following is not possible?
A)both have the same mean,but different standard deviations
B)both have the same standard deviation,but different means
C)both have the same mean and the same standard deviation
D)both have different means and different standard deviations
E)all of these are possible

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Q 69Q 69

When referring to qualitative variables,maximum variability occurs when
A)the standard deviation is a large number.
B)the number of individuals is evenly divided among the possible categories.
C)all of the individuals fall into a single category.
D)none of these

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Multiple Choice

Q 70Q 70

If a distribution is positively skewed,this means that
A)the scores tend to be clustered towards the high end of the scale.
B)the scores tend to be clustered towards the low end of the scale.
C)the scores are positive numbers.
D)the distribution is highly peakeD.

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Multiple Choice

Q 71Q 71

The symbol used for the population variance is _____ and the symbol used for the population standard deviation is _____.
A)s;s

^{2}B)s^{2},s C)s;s^{2}D)s^{2};sFree

Multiple Choice

Q 72Q 72

Measures of Central tendency are an example of_____.
A)inferential statistics
B)descriptive statistics
C)nonparametric statistics
D)both descriptive and nonparametric statistics

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Multiple Choice

Q 73Q 73

_____refer(s)to the tendency for scores to cluster on one side of the mean in some distributions.
A)Unbalancing
B)Skewness
C)Kurtosis
D)Both skewness and kurtosis
E)None of these

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Multiple Choice

Q 74Q 74

What statement below is TRUE in regards to a normal distribution?
A)Distribution unequal
B)Scores are skewed
C)Mean,median and mode are equal
D)Theoretical in nature
E)Both c & d

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Multiple Choice

Q 75Q 75

Measures of central tendency include the following EXCEPT _____.
A)mean
B)median
C)mode
D)range
E)All of these are measures of central tendency.

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Multiple Choice

Q 76Q 76

Eight psychology students took a well-known I.Q.test and achieved the following scores: 96,98,108,110,115,120,121,142.The mean I.Q.is _____.
A)130
B)113.80
C)113.75
D)115
E)None of these

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Multiple Choice

Q 77Q 77

Which of the following statements is true about the median?
A)It divides a distribution in half.
B)It may not have been a score actually in the distribution
C)Approximately 50% of the scores will be above the median and 50% below.
D)All of these are correct.

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Multiple Choice

Q 78Q 78

If a distribution is less peaked than another,it is said to be more____;if it is more peaked than another,it is said to be more_____.
A)Skewed;variable
B)Leptokuritc;variable
C)platykurtic;leptokurtic
D)leptokurtic;platykurtic

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Multiple Choice

Q 79Q 79

What measure of central tendency is used with a nominal scale?
A)Mean
B)Median
C)Mode
D)Both mean and mode
E)All of these

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Multiple Choice

Q 80Q 80

The mean of a _____skewed distribution will always be _____than the median.
A)positively;less
B)negatively;less
C)negatively;greater
D)normal;less

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Q 81Q 81

The class exam one in your statistics course indicates the Mean was 75 the Median was 78 and the Mode 79.50.This indicates a _____distribution.
A)normal
B)negatively skewed
C)positively skewed
D)None of these

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Q 82Q 82

Dr.Qui found his test scores to be as follows 60,92,75,79,75,and 90.What is the range of the test scores?
A)30
B)32
C)75
D)None of these

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Multiple Choice

Q 83Q 83

What measures are used to determine the amount of variability that occurs in a data set?
A)Variance
B)Standard Deviation
C)Mean
D)Both Variance and Standard Deviation
E)All of these

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Q 84Q 84

The _____tells us the average variability in a cluster of scores.
A)variance
B)standard deviation
C)mean
D)Both Variance and Standard Deviation
E)All of these

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Q 85Q 85

John waited an average of 5 minutes at a local Starbucks for his coffee with a SD of 2.00.On campus he waits 4 minutes for coffee with a SD of 3.00.What coffee vendor has more variability in its distribution of coffee?
A)The local Starbucks
B)The campus coffee house
C)They are equal
D)None of these

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Q 86Q 86

It has been reported the mean driving speed in California is 70 mph and the variance is 9.What is the SD?
A)9
B)3
C)8.5
D)None of these

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Q 87Q 87

The average person can hold 7+2 digits or bits of information in their short term memory with an SD= 2.What is the variance?
A)9
B)4
C)7
D)None of these

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Multiple Choice

Q 88Q 88

In real estate the Median house price is reported rather than the mean because_____.
A)it helps sale houses
B)it is not affected by extreme house prices
C)it indicates that 50% houses cost more and 50% cost less
D)Both b & c
E)All of these

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Q 89Q 89

In APA journal articles the results sections usually report the _____and_____of the data set.
A)mean;variance
B)mean;SD
C)median;SD
D)median;variance

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Q 90Q 90

A distribution that has a mean of 10 SD of 5 is much more_____than a distribution with a mean of 10 and SD of 2.
A)leptokurtic
B)platykurtic
C)skewed
D)None of these

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True False

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True False

Q 94Q 94

If we were to randomly select one score from a set of scores,the value of that score
would most likely be equal to the mode as opposed to any other value.

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True False

Q 95Q 95

The major problem with the mode as a measure of central tendency is that there can be
only one modal score.

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True False

Q 96Q 96

The median is the point in the distribution of scores that divides the distribution into two equal parts.

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True False

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True False

Q 98Q 98

The formula for computing the median is based on the assumption that the median occurs within the real limits of the middle score(s).

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True False

Q 99Q 99

Across all individuals,scores will always be closest to the mode than any other index of central tendency.

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True False

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True False

Q 101Q 101

The mean is computed by summing all of the scores and then dividing the sum by the
squared deviation scores.

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True False

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True False

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True False

Q 104Q 104

In practice,the three measures of central tendency will almost always be equal to one another.

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True False

Q 105Q 105

Most of the inferential statistics used by behavioral scientists make use of the median as a measure of central tendency.

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True False

Q 106Q 106

Ideally,when trying to characterize a set of scores,it is useful to report all three indices of central tendency.

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True False

Q 107Q 107

The more extreme a score is relative to the other scores in the distribution,the less it will change the value of the mean if it is deleted from the analysis.

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True False

Q 108Q 108

When a quantitative variable is measured on an ordinal level that departs markedly from interval characteristics,the mean is the most meaningful measure of central tendency.

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True False

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True False

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True False

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True False

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True False

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True False

Q 114Q 114

The interquartile range is the difference between the highest and lowest scores after the top 75% of the scores and the bottom 75% of the scores have been eliminated from the data.

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True False

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True False

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True False

Q 117Q 117

When the mean and median are different,the sum of the squared deviations from the mean will always be less than the sum of the squared deviations from the median.

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True False

Q 118Q 118

The sum of squared deviations from the mean will always be greater than the sum of squared deviations around any other index of central tendency.

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True False

Q 119Q 119

One problem with the sum of squares as an index of variability is that its size depends not only on the amount of variability among scores,but also on the number of scores (N).

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True False

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True False

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True False

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True False

Q 123Q 123

When variables are measured on an ordinal level that departs markedly from interval characteristics,the standard deviation is the best measure of variability.

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True False

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True False

Q 125Q 125

Most scores in negatively skewed distributions occur below the mean and only a relatively few extreme scores occur above it.

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True False

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True False

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True False

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True False

Q 129Q 129

The median is used when there are extreme scores for example income levels or house prices.

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True False

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Q 131Q 131

The shape of a distribution is influenced by both the variance with in the data set and the mean median and mode.

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True False

Q 132Q 132

If you were measuring the income level of people living in Los Angeles you would use the median because____________________.

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Q 134Q 134

The measure of central tendency not affected by extreme scores is the____________________.

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Q 136Q 136

The mean for class A's exam was 76 and the SD is 4.The mean for class B's exam was 78 and the SD is 8.Class ____________________has more variance on the exam.

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Q 137Q 137

The measure of central tendency that is used with qualitative data is____________________.

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Q 139Q 139

What type of graph uses medians and interquartile ranges rather than means and standard deviations ____________________.

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Q 141Q 141

The sum of squares for a data set is 144 which has 80 subjects in it,what is the SD is____________________.

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Q 146Q 146

Explain why the mean is not an optimal measure of central tendency when there are one or more extreme scores in the distribution.

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Q 150Q 150

Define skewness and describe what is meant by positively and negatively skewed distributions.

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Q 152Q 152

Fill in the following table.
What is the median of the distribution or 50

^{th}percentile?Free

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Q 153Q 153

Consider the 2 sets of data below and calculate the mean,median,mode and range for each.
A.20 19 21 20 10 300
B.53 54 55 56 57 59 60

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Q 154Q 154

For the following set of scores compute the mean,mode,sum of squares,variance and standard deviation: 30 32 34 40 50 45 46 47

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