Deck 4: Variability

Question 1

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

Answer 1

​1.5

Question 2

What are the values for SS (sum of squared deviations)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

Answer 2

​SS = 9 and variance = 3

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)​20

Answer 3

​13

Question 4

What is the value of SS (sum of squared deviations)for the following set of scores? Scores: 8,3,1​

A)​26
B)​29
C)​74
D)​144

Question 5

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 6

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)​16

Question 7

A population has sum of squared deviations,SS = 100 and variance,s2 = 4.What is the value of S(X - m)for the population?​

A)​0
B)​25
C)​100
D)​400

Question 8

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 9

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 10

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 11

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

A)​17
B)​18
C)​42
D)​10

Question 12

What is the value of SS (sum of squared deviations)for the following set of scores? If the scores constitute a population,what is the population standard deviation,s? Scores: 1,1,4,0.​

A)​SS = 9 and s = 2
B)​SS = 16 and s = 2
C)​SS = 9 and s = 1.5
D)​SS = 16 and s = 1.5

Question 13

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)​less than 50
C)​greater than 50
D)​0

Question 14

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 15

A population has sum of squared deviations,SS = 100 and variance,s2 = 4.How many scores are in the population?​

A)​25
B)​26
C)​200
D)​400

Question 16

A sample of n = 9 scores has a variance of s² = 144.What is the standard deviation for this sample?​

A)​s=19
B)​s=12
C)​s=16
D)​s=14

Question 17

Which of the following symbols identifies the population standard deviation?​

A)​s
B)​s²
C)​σ
D)​σ2

Question 18

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

A)2​
B)​4
C)​8
D)​16

Question 19

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 20

A population of N = 5 scores has ΣX = 20 and ΣX2 = 100.For this population,what is the value of SS (sum of squared deviations)?​

A)​20
B)​80
C)​100
D)​380

Question 21

You have a score of X = 65 on a math exam.The mean score for the class on the exam is μ = 70.Which of the following values for the standard deviation would give you the most favorable position within the class?​

A)​σ = 0
B)​σ = 1
C)​σ = 5
D)​σ = 10

Question 22

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 23

A sample of n = 5 scores has ΣX = 20 and ΣX² = 180.For this sample,what is the value of the sample standard deviation,s?​

A)5​
B)8
C)12
D)20

Question 24

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 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 the____.​

A)​mean is greater than 10
B)​standard deviation is smaller than 5
C)​standard deviation is less than 6
D)​standard deviation is greater than 6

Question 26

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 27

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

A)​3
B)​4.5
C)​9
D)​81

Question 28

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 29

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 30

There is a six-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 31

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 32

For a particular sample of size n=10,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 will be ____.​

A)​less than 4
B)​between 4 and 11
C)​greater than 11
D)​equal to 0

Question 33

A sample of n = 4 scores has ΣX = 8 and ΣX² = 40.What is the value of the sample variance,s²?​

A)​2
B)​4
C)​8
D)​10

Question 34

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 35

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

A)​2
B)​8
C)​15
D)​16

Question 36

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 37

Given a population with mean m = 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 = 2
B)​σ = 3
C)​σ = 5
D)​σ = 12

Question 38

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)​28

Question 39

You have a score of X = 75 on a statistics exam.The mean score for the class on the exam is μ = 70.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)​σ = 12

Question 40

Which of the following symbols identifies the sample variance?​

A)​s
B)​s²
C)​Σ
D)​σ2

Question 41

Variability provides a quantitative measure of the difference between scores in a distribution.​

Question 42

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.​

Question 43

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

Question 44

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

Question 45

If the population standard deviation is 4,then the variance will be σ² = 16.​

Question 46

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

Question 47

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

Question 48

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

Question 49

For a sample of n = 6 scores with ΣX = 30 and ΣX² = 200,SS = 20.​

Question 50

For a population of N = 4 scores with ΣX = 10 and ΣX² = 30,SS = 5.​

Question 51

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

Question 52

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

Question 53

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

Question 54

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

Question 55

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

Question 56

The range and the standard deviation are both measures of spread.​

Question 57

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

Question 58

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

Question 59

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

Question 60

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 61

Calculate the variance and the standard deviation for the following sample data.Scores: 10,7,9,1,2,0,6​

Question 62

For the following sample,use the computational formula to calculate SS.Then,compute the sample variance and standard deviation.​Scores: 1,3,1,1

Question 63

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

Question 64

Without some correction,sample variability is said to be "biased." Define the term biased,and explain how this bias is corrected in the formula for sample variance.​

Question 65

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 66

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 67

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

Question 68

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 69

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

Question 70

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

Question 71

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

Question 72

Using the definitional formula,compute SS,variance and the standard deviation for the following sample of scores.​Scores: 3,6,1,6,5,3

Question 73

For each of the following samples: Sample #1: 1,0,3,6Sample #2: 1,3,5,4,7
a. Compute the mean.
b. Determine whether it would be better to use the computational or the definitional formula for SS.
c. Compute the SS.

Question 74

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

Question 75

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