Deck 4: Measures of Variability

Question 1

A population has SS = 100 and $\sigma$ ² = 4.What is the value of $\Sigma$ (X - $\mu$ )for the population?

A)0
B)25
C)100
D)400

Answer 1

0

Question 2

What is the value of SS for the following set of scores? Scores: 0,1,4,5

A)17
B)18
C)42
D)Cannot answer without knowing whether it is a sample or a population

Answer 2

A

Question 3

A population of N = 5 scores has ΣX = 20 and ΣX² = 100.For this population,what is the value of SS?

A)20
B)80
C)100
D)380

Answer 3

A

Question 4

For the following scores,which of the following actions will increase the range?

A)Subtract 3 points from the score X = 3 Scores: 3,7,10,15
B)Subtract 3 points from the score X = 7
C)Subtract 3 points from the score X = 10
D)Subtract 3 points from the score X = 15

Question 5

For a particular population,the largest distance (deviation)between a score and the mean is 11 points.The smallest distance between a score and the mean is 4 points.Therefore,the standard deviation _____.

A)will be less than 4
B)will be between 4 and 11
C)will be greater than 11
D)It is impossible to say anything about the standard deviation.

Question 6

In a population of N = 10 scores,the smallest score is X = 8 and the largest is X = 20.What is the range for this population?

A)8
B)10
C)12-13
D)20

Question 7

Which of the following is a consequence of increasing variability?

A)The distance from one score to another tends to increase,and a single score tends to provide a more accurate representation of the entire distribution.
B)The distance from one score to another tends to increase,and a single score tends to provide a less accurate representation of the entire distribution.
C)The distance from one score to another tends to decrease,and a single score tends to provide a more accurate representation of the entire distribution.
D)The distance from one score to another tends to decrease,and a single score tends to provide a less accurate representation of the entire distribution.

Question 8

Which set of scores has the smallest standard deviation?

A)11,17,31,53
B)5,11,42,22
C)145,143,145,147
D)27,105,10,80

Question 9

A population has SS = 100 and $\sigma$ ² = 4.How many scores are in the population?

A)25
B)26
C)200
D)400

Question 10

What is the value of SS for the following set of scores? Scores: 8,3,1.

A)26
B)29
C)74
D)144

Question 11

What is the range for the following set of scores? Scores: 5,7,9,15

A)4 points
B)5 points
C)10 or 11 points
D)15 points

Question 12

A set of scores ranges from a high of X = 34 to a low of X = 24 and has a mean of 29.Which of the following is the most likely value for the standard deviation for these scores?

A)2 points
B)5 points
C)10 points
D)34 points

Question 13

What is the value of SS (sum of squared deviations)for the following population? Population: 1,1,1,5

A)3
B)7
C)12
D)28

Question 14

A sample consists of n = 16 scores.How many of the scores are used to calculate the range?

A)2
B)4
C)8
D)All 16

Question 15

What is the value of SS for the following set of scores? Scores: 1,1,4,0

A)18
B)10
C)9
D)6

Question 16

The sum of the squared deviation scores is SS = 20 for a population of N = 5 scores.What is the variance for this population?

A)4
B)5
C)80
D)100

Question 17

What is the value of SS (sum of squared deviations)for the following population? Population: 2,3,0,5

A)13
B)38
C)13/4 = 3.25
D)38/4 = 9.50

Question 18

A population of N = 6 scores has ΣX = 12 and ΣX² = 54.What is the value of SS for this population?

A)5
B)9
C)30
D)54

Question 19

A population of N = 100 scores has µ = 30 and σ = 4.What is the population variance?

A)2
B)4
C)8
D)16

Question 20

Which of the following symbols identifies the population standard deviation?

A)s
B)s²
C)σ
D)σ ²

Question 21

What is the variance for the following population of scores? Scores: 5,2,5,4

A)6
B)2
C)1.5
D)1.22

Question 22

A sample of n = 5 scores has ΣX = 20 and ΣX² = 120.For this sample,what is the value of SS?

A)20
B)40
C)100
D)120

Question 23

What is the value of SS (sum of squared deviations)for the following sample? Sample: 1,3,2,2

A)0.50
B)2
C)4
D)18

Question 24

If sample variance is computed by dividing SS by df = n - 1,then the average value of the sample variances from all possible random samples will be _______ the population variance.

A)smaller than
B)larger than
C)exactly equal to
D)unrelated to

Question 25

A sample of n = 8 scores has SS = 50.If these same scores were a population,then the SS value for the population would be _____.

A)50
B)greater than 50
C)less than 50
D)impossible to determine without additional information

Question 26

A sample of n = 4 scores has ΣX = 8 and ΣX² = 40.What is the value of SS for this sample?

A)6
B)8
C)24
D)40

Question 27

A sample of n = 25 scores has M = 20 and s² = 9.What is the sample standard deviation?

A)3
B)4.5
C)9
D)81

Question 28

Under what circumstances is the computational formula preferred over the definitional formula when computing SS,the sum of the squared deviations,for a sample?

A)When the sample mean is a whole number
B)When the sample mean is not a whole number
C)When the sample variance is a whole number
D)When the sample variance is not a whole number

Question 29

What are the values for SS and variance for the following sample of n = 3 scores? Sample: 1,4,7

A)SS = 18 and variance = 6
B)SS = 18 and variance = 9
C)SS = 66 and variance = 22
D)SS = 66 and variance = 33

Question 30

The sum of the squared deviation scores is SS = 20 for a sample of n = 5 scores.What is the variance for this sample?

A)4
B)5
C)80
D)100

Question 31

Which of the following symbols identifies the sample variance?

A)s
B)s²
C)σ
D)σ ²

Question 32

What is the value of SS (sum of squared deviations)for the following sample? Sample: 1,1,1,7

A)52
B)27
C)25
D)9

Question 33

A sample of n = 6 scores has a standard deviation of s = 3.What is the value of SS,the sum of the squared deviations for this sample?

A)54
B)45
C)18
D)15

Question 34

A researcher takes a sample from a population and computes a statistic for the sample.Which of the following statements is correct?

A)If the sample statistic overestimates the corresponding population parameter,then the statistic is biased.
B)If the sample statistic underestimates the corresponding population parameter,then the statistic is biased.
C)If the sample statistic is equal to the corresponding population parameter,then the statistic is unbiased.
D)None of the other statements is correct.

Question 35

All the possible samples of n = 3 scores are selected from a population with $\mu$ = 30 and $\sigma$ = 5 and the mean is computed for each of the samples.If the average is calculated for all of the sample means,what value will be obtained?

A)30
B)Greater than 30
C)Less than 30
D)Impossible to predict

Question 36

If sample variance is computed by dividing SS by n,then the average value of the sample variances from all the possible random samples will be _______ the population variance.

A)smaller than
B)larger than
C)exactly equal to
D)unrelated to

Question 37

A sample of n = 9 scores has a variance of s² = 18.If the scores were a population,what value would be obtained for the population variance.

A) $\sigma$ ² = 14
B) $\sigma$ ² = 16
C) $\sigma$ ² = 24
D) $\sigma$ ² = 144

Question 38

A set of 10 scores has SS = 90.If the scores are a sample,the sample variance is ____,and if the scores are a population,the population variance is ____.

A)s² = 9; σ² = 9
B)s² = 9; σ² = 10
C)s² = 10; σ² = 9
D)s² = 10; σ² = 10

Question 39

A population of N = 10 scores has a standard deviation of $\sigma$ = 2.What is the value of SS,the sum of the squared deviations,for this population?

A)40
B)20
C)4
D)2

Question 40

What are the values for SS and variance for the following sample of n = 4 scores? Sample: 1,1,0,4

A)SS = 9 and variance = 3
B)SS = 9 and variance = 2.25
C)SS = 18 and variance = 6
D)SS = 18 and variance = 9

Question 41

A population with SS = 90 and a variance of 9 has N = 10 scores.

Question 42

A population has µ = 50 and σ = 5.If 10 points are added to every score in the population,what are the new values for the mean and standard deviation?

A)µ = 50 and σ = 5
B)µ = 50 and σ = 15
C)µ = 60 and σ = 5
D)µ = 60 and σ = 15

Question 43

On an exam with a mean of μ = 70,you have a score of X = 75.Which of the following values for the standard deviation would give you the highest position within the class?

A)σ = 1
B)σ = 5
C)σ = 10
D)Cannot determine from the information given

Question 44

The range and the standard deviation are both measures of distance.

Question 45

A population of scores has µ = 50 and σ = 5.If every score in the population is multiplied by 3,then what are the new values for the mean and standard deviation?

A)µ = 50 and σ = 5
B)µ = 50 and σ = 15
C)µ = 150 and σ = 5
D)µ = 150 and σ = 15

Question 46

The range is usually considered to be a relatively crude measure of variability.

Question 47

Which of the following actions will have no effect on the value of the standard deviation?

A)Multiply each score in the distribution by 2
B)Divide each score in the distribution by 2
C)Subtract 5 points from every score in the distribution
D)All of the other actions will change the value of the standard deviation

Question 48

For a population of N = 4 scores with $\Sigma$ X = 10 and $\Sigma$ X² = 30,SS = 5.

Question 49

A positive deviation always indicates a score that is less than the mean.

Question 50

There is a 6-point difference between two sample means.If the two samples have the same variance,which of the following values would make the mean difference easiest to see in a graph showing the two distributions?

A)s² = 2
B)s² = 8
C)s² = 16
D)s² = 64

Question 51

To calculate the variance for a population,SS is divided by N.

Question 52

Which of the following is true for most distributions?

A)Around 30% of the scores will be located within one standard deviation of the mean.
B)Around 50% of the scores will be located within one standard deviation of the mean.
C)Around 70% of the scores will be located within one standard deviation of the mean.
D)Around 90% of the scores will be located within one standard deviation of the mean.

Question 53

For a population of scores,the sum of the deviation scores is equal to N.

Question 54

Under what circumstances would a score that is 10 points below the mean be considered to be an extreme value?

A)When the mean is much greater than 10
B)When the mean is much less than 10
C)When the standard deviation is much greater than 10
D)When the standard deviation is much less than 10

Question 55

On an exam with a mean of μ = 70,you have a score of X = 65.Which of the following values for the standard deviation would give you the highest position within the class?

A)σ = 1
B)σ = 5
C)σ = 10
D)Cannot determine from the information given

Question 56

The value for SS can never be less than zero.

Question 57

For a population,a deviation score is computed as X - μ.

Question 58

If the highest score in a distribution is X = 16 and the lowest is X = 4,then the range is 12 or 13 points.

Question 59

For a population with $\mu$ = 60,which of the following values for the population standard deviation would cause X = 68 to have the most extreme position in the distribution?

A)σ = 1
B)σ = 2
C)σ = 3
D)σ = 4

Question 60

One sample is selected to represent scores in treatment 1 and a second sample is used to represent scores in treatment 2.Which set of sample statistics would present the clearest picture of a real difference between the two treatments?

A)M₁ = 36,M₂ = 40,and both variances = 43
B)M₁ = 36,M₂ = 40,and both variances = 6
C)M₁ = 38,M₂ = 40,and both variances = 43
D)M₁ = 38,M₂ = 40,and both variances = 6

Question 61

It is easier to see the mean difference between two samples if the sample variances are small.

Question 62

In a population with a mean of μ = 40 and a standard deviation of σ = 8,a score of
X = 46 would be an extreme value,far out in the tail of the distribution.

Question 63

To calculate the variance for a sample,SS is divided by df = n - 1.

Question 64

After a researcher multiplies every score in a sample by 2,the standard deviation is found to be s = 10.The original sample had a standard deviation of s = 5.

Question 65

If you have a score of X = 76 on an exam with $\mu$ = 70,you should expect a better grade if σ = 10 than if σ = 5.

Question 66

If the population variance is 5,then the population standard deviation is σ = 25.

Question 67

Multiplying every score in a sample by 3 will not change the value of the standard deviation.

Question 68

If the scores in a population range from a low of X = 5 to a high of X = 14,then the population standard deviation must be less than 10 points.

Question 69

A sample of n = 6 scores has SS = 30 and s² = 6.If the 6 scores were a population,the value of SS would still be 30,but the variance would be σ² = 5.

Question 70

For a population with µ = 70 and σ = 5,about 95% of the individuals will have scores between X = 65 and X = 75.

Question 71

If the population variance is 4,then the standard deviation will be σ = 16.

Question 72

For a sample with M = 20 and s = 4,a score of X = 17 would be considered an extremely low score.

Question 73

After a researcher adds 5 points to every score in a sample,the standard deviation is found to be s = 10.The original sample had a standard deviation of s = 5.

Question 74

A sample of n = 25 scores is selected from a population with a variance of σ² = 16,and the variance is computed for the sample using n - 1.The sample variance probably will be smaller than 16.

Question 75

If a sample of n = 6 scores has $\Sigma$ X = 30 and $\Sigma$ X² = 200,then SS = 20.

Question 76

If you have a score of X = 66 on an exam with $\mu$ = 70,you should expect a better grade if σ = 10 than if σ = 5.

Question 77

A sample of n = 7 scores has SS = 42.The variance for this sample is s² = 6.

Question 78

For a sample with M = 40 and s = 4,about 95% of the individuals will have scores between X = 32 and X = 48.

Question 79

A sample with a variance of 25 has a standard deviation equal to 5 points.

Question 80

A sample with SS = 40 and a variance of 8 has n = 5 scores.