Deck 4: Exploring Data: Variability

Question 1

The range is the distance between the two extreme scores.

Answer 1

True

Question 2

The most widely used measure of variability is the range.

Answer 2

False

Question 3

Finding the interquartile range first requires a calculation of percentiles.

Answer 3

True

Question 4

Calculating a deviation score requires a standard deviation.

Question 5

The formula for the standard deviation of a sample used to estimate ? has N in the denominator.

Question 6

Your text identifies three different standard deviations.

Question 7

An error is indicated when the sum of the deviation scores for a distribution is 0.

Question 8

The text uses a bar graph and error bars to show a mean and standard deviation on a single graph.

Question 9

The range is the distance between the two extreme scores divided by 2.

Question 10

The interquartile range is 0.25 times the range.

Question 11

Calculating a deviation score requires the interquartile range.

Question 12

The formula for the standard deviation of a population has N in the denominator.

Question 13

An error is indicated if the sum of the deviation scores for a distribution is a negative number.

Question 14

A standard deviation equal to 0 is an impossible value.

Question 15

A squared standard deviation is called a variance.

Question 16

The text uses a pie chart to show a mean and standard deviation on a single graph.

Question 17

To find the range multiply the interquartile range by 2.

Question 18

The most widely used measure of variability is the interquartile range.

Question 19

Calculating a deviation score requires a mean.

Question 20

The formula for the standard deviation of a sample used to estimate ? has N -1 in the denominator.

Question 21

Three different standard deviation formulas re used to indicate variability about the mean, median, and mode, respectively.

Question 22

The sum of the deviation scores for a distribution is 0 when all calculations are correct.

Question 23

An error is indicated if a standard deviation is equal to a negative number.

Question 24

To calculate a variance of a distribution, double the standard deviation of the distribution.

Question 25

The text uses a bimodal curve to show a mean and standard deviation on a single graph.

Question 26

Data Set 4-1: 2, 7, 3, 6, 2

-For Data Set 4-1, find the standard deviation $\sigma$ .

A) 2.10
B) 2.05
C) 4.40
D) 4.69.

Question 27

Data Set 4-1: 2, 7, 3, 6, 2

-For Data Set 4-1, the range is

A) 7
B) 6
C) 5
D) 20.

Question 28

Data Set 4-1: 2, 7, 3, 6, 2

-For Data Set 4-1, the population variance is

A) 2.05
B) 4.20
C) 4.40
D) 22.

Question 29

Data Set 4-2: 5, 3, 9, 7, 6

-Referring to Data Set 4-2, the range is

A) 2
B) 5
C) 6
D) 7.

Question 30

Data Set 4-2: 5, 3, 9, 7, 6

-You can just look at the scores 10, 11, 9, 10, 11, 9 and see that they are ______ than Data Set 4-2.

A) more variable
B) less variable
C) equally as variable.

Question 31

Data Set 4-2: 5, 3, 9, 7, 6

-If you consider Data Set 4-2 to be a population, the standard deviation is

A) 4.00
B) 2.24
C) 2.00
D) 0.

Question 32

Data Set 4-2: 5, 3, 9, 7, 6

-The raw score of 7 in Data Set 4-2 has a deviation score of

A) 0
B) 1
C) 2
D) 7.

Question 33

Data Set 4-3: -2, -1, 0, 2, 6

-Refer to Data Set 4-3. The standard deviation S is

A) 2.58
B) 2.83
C) 6.67
D) none of the above

Question 34

Data Set 4-3: -2, -1, 0, 2, 6

-Which of the following distributions is more variable than Data Set 4-3? (You should be able to answer by just eyeballing the numbers.)

A) 2, 1, 0, 1, 2, 6
B) 0, 1, 2, 3, 4, 6
C) -1, -1, 0, 1, 1
D) none of the other alternatives are correct

Question 35

Data Set 4-3: -2, -1, 0, 2, 6

-Refer to Data Set 4-3. The range is

A) 6
B) 7
C) 8
D) 9.

Question 36

Data Set 4-5: 2, 4, 6, 8

-Refer to Data Set 4-5. The range is

A) 6
B) 7
C) 5
D) not enough information is given.

Question 37

Data Set 4-5: 2, 4, 6, 8

-Refer to Data Set 4-5. If these scores were a sample from a larger population to which you wished to generalize, the standard deviation is

A) 6.67
B) 5.00
C) 2.58
D) 2.24.

Question 38

Data Set 4-5: 2, 4, 6, 8

-Which of the following distributions is more variable than Data Set 4-5? (You should be able to answer just by eyeballing the numbers.)

A) 3, 5, 7, 9
B) -2, 0, 2, 4
C) 10, 11, 12, 13
D) none of the above

Question 39

Data Set 4-6: -1, 3, 0, 2, 1

-Referring to Data Set 4-6, the range is

A) 5
B) 4
C) 3
D) none of the other alternatives are correct.

Question 40

Data Set 4-6: -1, 3, 0, 2, 1

-In Data Set 4-6 the score of 0 has a deviation score of

A) 0
B) 1
C) - 1
D) 5.

Question 41

Data Set 4-6: -1, 3, 0, 2, 1

-Suppose the scores in Data Set 4-6 were ratings of five freshmen. A question arose about the standard deviation of the ratings of the entire class and these five were taken to be a representative sample. The standard deviation is

A) 2.50
B) 1.99
C) 1.58
D) 1.41.

Question 42

Data Set 4-6: -1, 3, 0, 2, 1

-Which of the following distributions of scores is less variable than Data Set 4-6? (You should be able to answer by just by eyeballing the numbers.)

A) 3, -2, -2, -1, 0
B) 0, -3, 3, 2, -2
C) 2, 4, 6, 8, 10
D) none of the other alternatives are correct.

Question 43

Data Set 4-7: These are all the scores that exist for an entire group. 1, 0, 5, 6

-The standard deviation of the scores in Data Set 4-7 is

A) 2.55
B) 2.94
C) 6.50
D) 8.67

Question 44

Data Set 4-7: These are all the scores that exist for an entire group. 1, 0, 5, 6

-The range for Data Set 4-7 is

A) 5
B) 6
C) 7
D) 8

Question 45

Data Set 4-7: These are all the scores that exist for an entire group. 1, 0, 5, 6

-A raw score of 6 in Data Set 4-7 has a deviation score of

A) 1
B) 0.0
C) -1
D) none of the other alternatives are correct.

Question 46

Data Set 4-8: 2, -2, 4, 6

-Using Data Set 4-8 as a sample, estimate the population.

A) 1.66
B) 2.96
C) 3.42

Question 47

Data Set 4-8: 2, -2, 4, 6

-For Data Set 4-8, a raw score of zero would have a deviation score of

A) 0
B) -3.5
C) -2.5
D) -0.85.

Question 48

Data Set 4-8: 2, -2, 4, 6

-For Data Set 4-8, the range is

A) 4
B) 5
C) 8
D) 9.

Question 49

Data Set 4-8: 2, -2, 4, 6

-The value of $\sigma$ ² for Data Set 4-8 is

A) 2.75
B) 8.75
C) 11.67

Question 50

Which of the following distribution of scores is the most variable?

A) 1, 2, 3
B) 8, 9, 10
C) 1, 3, 5
D) all of the other alternatives are equally variable.

Question 51

Which of the following distributions is the least variable?

A) 2, 1, 0, 1, 2
B) -2, -1, 0, 1, 2
C) 1, 2, 3, 4, 5
D) none of the other alternatives, all are equally variable.

Question 52

Which of the following distributions of scores is the least variable?

A) 0, 1, 2
B) -2, 0, 2
C) 1, 2, 2
D) all of the other alternatives are equally variable.

Question 53

Which of the following contains an expression of variability about Joe?

A) "Joe is solid as a rock you can count on him."
B) "For his dental appointments, Joe is always late."
C) "Sometimes Joe's ideas are great and sometimes they're off the wall."
D) "He's absolutely the most undisciplined person on the staff."

Question 54

Which of the following statements is concerned with variability?

A) Whatever will be, will be.
B) A friend in need is a friend indeed.
C) It is not possible to step twice in the same river.
D) Haste makes waste.

Question 55

Which of the following statements is false, according to your text?

A) The salaries of people in sales are more variable than those in management.
B) For a distribution of scores, $\hat { S }$ is smaller than S.
C) Males are more variable than females in reaching puberty.
D) none of the other alternatives are correct.

Question 56

Choose the statement that is true, according to your text.

A) The pay for people in management is more variable than the pay for those in sales.
B) $\hat { S }$ is a biased estimate of $\sigma$
C) In reaching puberty, males are more variable than females.
D) All of the other alternatives are correct.

Question 57

For the scores: 2, 3, 5, 7, the range is

A) 4
B) 5
C) 6
D) none of the other alternatives are correct.

Question 58

For the scores: 0, 2, 4, 5, the range is

A) 5
B) 4
C) 0
D) none of the other alternatives are correct.

Question 59

For the scores: -2, 0, 2, 5, the range is

A) a negative number
B) 6
C) 4
D) none of the other alternatives are correct.

Question 60

The statistic most descriptive of the middle 50 percent of the distribution is

A) the range
B) the interquartile range
C) $\hat { S }$
D) $\sigma$ .

Question 61

The interquartile range tells you the scores that were made bypercent of the distribution.

A) 25
B) 50
C) 95
D) 100.

Question 62

The interquartile range tells you something aboutof the scores of the distribution.

A) one-tenth
B) one-fourth
C) one-half
D) nine-tenths.

Question 63

The interquartile range always

A) is one-fourth of the range
B) becomes larger if more observations are added
C) contains 50 percent of the frequencies
D) all of the other alternatives are correct.

Question 64

Which of the following is needed in calculating the interquartile range of a distribution?

A) 50th percentile
B) 75th percentile
C) 95th percentile
D) all of the other alternatives are correct.

Question 65

The best estimate of the population standard deviation, calculated from a sample is

A) $\hat { s }$
B) S
C) $\sigma$
D) range.

Question 66

The standard deviation that estimates a population standard deviation from calculations on a sample is

A) $\sigma$
B) $\hat { S }$
C) S.

Question 67

The statistic that is an estimate of $\sigma$ ² is

A) $\Sigma$ X²
B) ( $\Sigma$ X)²
C) $\hat { S }$
D) none of the other alternatives are correct.

Question 68

The statistic that is used to estimate $\sigma$ is

A) $\hat { S }$
B) S
C) $\Sigma$ X/N
D) none of the other alternatives are correct.

Question 69

An investigator wanted an estimate of the variance of a population. She drew a sample. Her last step would be to calculate

A) $\sigma$
B) $\sigma$ ²
C) $\hat { S }$
D) $\hat{ S }$ ².

Question 70

From all the employees in a company, a small group was selected to participate in a study of employee satisfaction. The results of the study were to be generalized to all the employees of the company. To find the variability in satisfaction, the investigator should compute

A) $\bar { X }$
B) S
C) $\hat { S }$
D) $\sigma$ .

Question 71

Suppose you had a sample and you wanted to draw conclusions about the variability of a population. You should calculate

A) $\hat { S }$
B) S
C) deviation scores
D) the range.

Question 72

Which of the following is false?

A) $\hat{ S }$ is used to estimate $\sigma$ .
B) $\hat { S }$ uses N - 1 in the denominator
C) $\hat { S }$ < $\sigma$ when both are calculated on the same numbers
D) $\hat{ S }$ is based on a sample.

Question 73

For a set of scores the sum of the deviation scores will be zero

A) when half the scores are negative
B) when the mean is zero
C) only when the standard deviation is zero
D) always.

Question 74

When a standard deviation is squared, you get a number that is

A) twice as big
B) called the variance
C) both twice as big and called the variance
D) neither twice as big, nor called the variance.

Question 75

Which of the following is (are) not mathematically possible if only one distribution is being considered?

A) range = $\hat { S }$
B) range = $\bar { X }$
C) range = $\mu$

Question 76

For any distribution of scores, which of the following is numerically the smallest?

A) the sum of the deviation scores
B) range
C) standard deviation
D) variance.

Question 77

Suppose you had three numbers with a mean of 2. You calculated a deviation score for each of the three numbers and then added the deviation scores. The sum would be

A) 1
B) 2
C) 3
D) 0.

Question 78

Which of the following may be a negative number?

A) range
B) variance
C) deviation score
D) standard deviation.

Question 79

A negative number is possible when you calculate

A) the range
B) the interquartile range
C) the variance
D) a deviation score.

Question 80

A score minus the mean of the scores is

A) the standard deviation
B) the variance
C) a deviation score
D) the range.