Deck 4: Variability

Question 1

For a sample of n = 16 scores, how many scores are used to calculate the sample variance?

A)2
B)8
C)15
D)all 16

Answer 1

D

Question 2

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

Answer 2

C

Question 3

In a population of N = 10 scores, the smallest score is X = 8 and the largest score is X = 20.Using the concept of real limits, what is the range for this population?

A)11
B)12
C)13
D)cannot be determined without more information

Answer 3

C

Question 4

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

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

Question 5

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 6

Which of the following symbols identifies the sample variance?

A)s
B)s²
C)σ
D)σ ²

Question 7

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 8

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 9

What is the value of SS (sum of squared deviations) for the following sample? Sample: 2, 3, 4, 7

A)14/3 = 2.67
B)14
C)72
D)78

Question 10

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 11

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

A)0
B)1
C)3
D)12

Question 12

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 13

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 14

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 15

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 16

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

Question 17

Which of the following symbols identifies the population standard deviation?

A)s
B)s²
C)σ
D)σ ²

Question 18

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 19

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 20

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 21

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 22

There is a 6-point difference between two sample means.If the two samples have the same variance, then which of the following values for the variance 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 23

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 24

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 25

The smallest score in a population is X = 5 and the largest score is X = 10.Based on this information, you can conclude that ______.

A)the population mean is somewhere between 5 and 10.
B)the population standard deviation is smaller than 6.
C)the population mean is between 5 and 10, and the standard deviation is less than 6.
D)None of the other choices is correct.

Question 26

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 27

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 28

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 29

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.

Question 30

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 31

A population has µ = 50 and σ = 5.If 10 points are added to every score in the population, 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 = 60 and σ = 5
D)µ = 60 and σ = 15

Question 32

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 33

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 34

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 35

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)? = 1
B)? = 2
C)? = 3
D)? = 4

Question 36

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 37

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 38

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 39

If sample variance is computed by dividing SS by df = n - 1, 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 40

For a particular sample, 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 41

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

Question 42

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

Question 43

Using the concept of real limits, the range is 8 points for a set of scores that range from a high of X = 16 to a low of X = 8.

Question 44

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

Question 45

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

Question 46

A population of N = 5 scores has SS = 20 and σ² = 4.If the 5 scores were a sample, the value of SS would still be 20 but the variance would be s² = 5.

Question 47

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

Question 48

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

Question 49

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

Question 50

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 51

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 52

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

Question 53

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

Question 54

For a sample of n = 6 scores with $\sum$ X = 30 and $\sum$ X² = 200, SS = 20.

Question 55

A sample of n = 25 scores is selected from a population with a variance of σ² = 16.The sample variance probably will be smaller than 16.

Question 56

The value for SS is always greater than or equal to zero.

Question 57

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

Question 58

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

Question 59

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 15 points.

Question 60

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

Question 61

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

Question 62

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

Question 63

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

Question 64

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

Question 65

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

Question 66

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

Question 67

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

Question 68

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

Question 69

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 70

For a sample with M = 20 and s = 1, a score of X = 17 would be considered an extremely low score.