Deck 4: Measures of Central Tendency and Variability

Question 1

A distribution has a mean of 78 and a median of 92. This distribution is _________.

A) symmetrical
B) negatively skewed
C) positively skewed
D) not enough information given

Answer 1

negatively skewed

Question 2

Let's assume that we have determined the salary of all the professors at your school. In plotting the distribution of salaries we notice that it is positively skewed. For this distribution _________.

A) mean = median
B) mean
C) mean > median
D) can't tell from the information given

Answer 2

mean > median

Question 3

A history professor gives a quiz to his class and records the following scores: 13, 11, 11, 9, 12, 13, 16, 14, 11, 10, 8, 13, 20. The range for this distribution is _________.

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

Answer 3

12

Question 4

A history professor gives a quiz to his class and records the following scores: 13, 11, 11, 9, 12, 13, 16, 14, 11, 10, 8, 13, 20. The mode(s) for this distribution is(are) _________.

A) 11
B) 13
C) 11 and 13
D) there is no mode

Question 5

The most commonly encountered measure of central tendency is the _________.

A) mean
B) median
C) mode
D) standard deviation

Question 6

An industrial psychologist observed 8 drill-press operators for one working day. She recorded the number of times each operator pressed the "faster" button instead of the "stop" button to determine whether the design of the control panel was contributing to the high rate of accidents in the plant. The resulting scores were as follows: 5, 2, 8, 2, 3, 2, 4, 12 The mean for this distribution is _________.

A) 3.52
B) 5.43
C) 4.75
D) 4.15

Question 7

An industrial psychologist observed 8 drill-press operators for one working day. She recorded the number of times each operator pressed the "faster" button instead of the "stop" button to determine whether the design of the control panel was contributing to the high rate of accidents in the plant. The resulting scores were as follows: 5, 2, 8, 2, 3, 2, 4, 12 The standard deviation for this distribution is _________. Assume sample data.

A) 3.34
B) 5.81
C) 2.28
D) 3.58

Question 8

An industrial psychologist observed 8 drill-press operators for one working day. She recorded the number of times each operator pressed the "faster" button instead of the "stop" button to determine whether the design of the control panel was contributing to the high rate of accidents in the plant. The resulting scores were as follows: 5, 2, 8, 2, 3, 2, 4, 12 The median for this distribution is _________.

A) 2.00
B) 3.50
C) 3.00
D) 3.25

Question 9

The mean weight for team A with 15 members is 140 lbs., the mean weight for team B with 7 members is 135 lbs., and the mean weight for team C with 20 members is 160 lbs. The overall mean weight for all three teams is _________.

A) 145.00
B) 138.78
C) 148.69
D) 178.43

Question 10

On a physics exam, the instructor gives a bonus question worth 10 points. The class average (mean) without counting the bonus question is 83. If everyone gets the bonus question correct, the class mean would _________.

A) remain the same
B) equal 83 + 10/ N
C) equal 93
D) exceed the median

Question 11

A history professor gives a quiz to his class and records the following scores: 13, 11, 11, 9, 12, 13, 16, 14, 11, 10, 8, 13, 20. The variance for this distribution is _________. Assume sample scores.

A) 162.38
B) 9.01
C) 9.76
D) 9.60

Question 12

For any distribution of scores Σ( X - µ ) = _________.

A) 0
B) Σ X
C) 1
D)

Question 13

A history professor gives a quiz to his class and records the following scores: 13, 11, 11, 9, 12, 13, 16, 14, 11, 10, 8, 13, 20. The median for this distribution is _________.

A) 12
B) 11
C) 13
D) 16

Question 14

An industrial psychologist observed 8 drill-press operators for one working day. She recorded the number of times each operator pressed the "faster" button instead of the "stop" button to determine whether the design of the control panel was contributing to the high rate of accidents in the plant. The resulting scores were as follows: 5, 2, 8, 2, 3, 2, 4, 12 The variance for this distribution is _________. Assume sample data.

A) 33.75
B) 11.19
C) 12.79
D) 15.75

Question 15

A history professor gives a quiz to his class and records the following scores: 13, 11, 11, 9, 12, 13, 16, 14, 11, 10, 8, 13, 20. The mean for this distribution is _________.

A) 12.38
B) 13.42
C) 18.05
D) 11.50

Question 16

In a certain statistics course, four exams were given. Each student s grade was based on a weighted average of his exam scores. The first two tests had weights of 1, the third test had a weight of 2, and the final test had a weight of 3. The exam scores for one student are listed below. The student s overall average was _________.

A) 151.28
B) 86.44
C) 83.18
D) 47.52

Question 17

A history professor gives a quiz to his class and records the following scores: 13, 11, 11, 9, 12, 13, 16, 14, 11, 10, 8, 13, 20 . The standard deviation for this distribution is _________. Assume sample scores.

A) 3.12
B) 3.00
C) 13.26
D) 12.74

Question 18

An industrial psychologist observed 8 drill-press operators for one working day. She recorded the number of times each operator pressed the "faster" button instead of the "stop" button to determine whether the design of the control panel was contributing to the high rate of accidents in the plant. The resulting scores were as follows: 5, 2, 8, 2, 3, 2, 4, 12 The range for this distribution is _________.

A) 9
B) 10
C) 12
D) 2

Question 19

An industrial psychologist observed 8 drill-press operators for one working day. She recorded the number of times each operator pressed the "faster" button instead of the "stop" button to determine whether the design of the control panel was contributing to the high rate of accidents in the plant. The resulting scores were as follows: 5, 2, 8, 2, 3, 2, 4, 12 The mode for this distribution is _________.

A) 2
B) 3
C) 8
D) there is no mode

Question 20

Consider the following scores: 21, 22, 22, 0.1, 20, 25, 28, 26, 23, 19, 0.5. Which of the measures listed below would give the best description of the central tendency of these scores?

A) mean
B) variance
C) range
D) median

Question 21

Which of the following is not a property of the mean?

A) The mean is sensitive to the exact value of all the scores.
B) The sum of the deviations about the mean equals zero.
C) The sum of the squared deviations about the mean is a minimum.
D) The mean is most subject to sampling variation.
E) The mean is most affected by extreme scores.

Question 22

equals _______ .

A) ΣX ²
B) ΣX ² - ( ΣX )²/N
C) cannot be determined from information provided
D) sum of squares
E) ΣX ² - ( ΣX )²/N and sum of squares

Question 23

If a constant of 5 is subtracted from all of the scores, the standard deviation _________.

A) decreases by 5
B) decreases by
C) remains the same
D) decreases by 5/ N

Question 24

Which of the following do (does) not measure average dispersion?

A) standard deviation
B) range
C) sum of squares
D) range and sum of squares

Question 25

The mean is _______ sensitive to extreme scores than the median.

A) more
B) less
C) equally
D) The correct answer cannot be determined without the scores.

Question 26

equals _______ .

A) the sum of squares
B) 0
C) 1
D) cannot be determined

Question 27

If 5 points are added to each score in a distribution, which of the following will happen?

A) the mean will be unchanged
B) the standard deviation will be unchanged
C) the mode will be unchanged
D) the mean, median and mode will be unchanged
E) the mean, median and mode will change.

Question 28

In calculating the standard deviation of a sample, we use _________ in the denominator.

A) N
B) N -1
C) the sum of the weights
D) X

Question 29

Considering again the information in problem 40, what would be the effect of adding those same new scores on the value of s ?

A) increase s
B) decrease s
C) s would remain unchanged
D) cannot be determined from the information given

Question 30

If the distribution is symmetrical, which is the best measure of central tendency?

A) mode
B) median
C) mean
D) variance

Question 31

If s = 12 for a set of 200 scores and 5 points were subtracted from each of the scores, the new value of the standard deviation would be _________.

A) 12/5
B)
C) 12 - 5
D) 12

Question 32

If 10 points were added to each score in a distribution, which of the following will happen?

A) the mean will remain unchanged
B) the mode will remain unchanged
C) the standard deviation will be unchanged
D) the mean, median, and mode will remain unchanged

Question 33

Which of the following is not a measure of variability?

A) standard deviation
B) range
C) sum of squares
D) variance
E) all of these are measures of variability

Question 34

is called _________.

A) standard deviation
B) mean
C) variance
D) sum of squares
E) confusing

Question 35

Assume one has a set of 35 scores with = 100 and s = 9. If 5 scores, each equal to 100 were added to the distribution, what effect would this have on ?

A) increase
B) decrease
C) would remain unchanged
D) cannot tell

Question 36

In a bell-shaped distribution, _________.

A) median = mean
B) median > mean
C) median
D) standard deviation equals variance

Question 37

In a negatively skewed distribution, the mean will generally be _______ the median.

A) greater than
B) less than
C) equal to
D) can't tell from this information

Question 38

equals _______ .

A) 0
B) 1
C) the variance
D) cannot be determined from the information provided

Question 39

Which of the following is not a measure of central tendency?

A) mode
B) median
C) mean
D) standard deviation

Question 40

The most commonly encountered measure of variability is _________.

A) range
B) standard deviation
C) mean
D) mode

Question 41

The mode is used extensively in the behavioral sciences.

Question 42

Given the following set of scores X : 10, 12, 6, 8, 9, 11, 13, 13, 5, 0, 1 What is the variance?

A) 20.6
B) 4.54
C) 18.7
D) 4.3

Question 43

The overall mean does not take into account the different number of subjects in each group.

Question 44

Given the following set of scores X : 10, 12, 6, 8, 9, 11, 13, 13, 5, 0, 1 What is the mean?

A) 8.0
B) 11.0
C) 13.5
D) 6.0

Question 45

What is the appropriate symbol for the formula:

A) s
B) s²
C) σ
D) σ²

Question 46

It is possible to have a set of scores with three different values for central tendency.

Question 47

The equation for the sum of squares of a sample is ΣS = ΣX² - ( Σ X)²/N

Question 48

Given the following set of scores X : 10, 12, 6, 8, 9, 11, 13, 13, 5, 0, 1 What is the value of ?

A) 4.54
B) 206
C) 1
D) 0

Question 49

The overall mean is a weighted mean.

Question 50

The mean number of students in a classroom at school A is 32.5 and there are 25 classrooms. The mean number of students at school B is 29.6 in 12 classrooms. At school C the mean in each class is 15.3 for 10 classrooms. What is the mean number of students per classroom for all the schools combined?

A) 1320.7
B) 28.1
C) 25.7
D) 28.7

Question 51

Given the following set of scores X : 10, 12, 6, 8, 9, 11, 13, 13, 5, 0, 1 What is the mode?

A) 0
B) 6
C) 13
D) 9

Question 52

If the following scores were population scores X : 10, 12, 6, 8, 9, 11, 13, 13, 5, 0, 1 What would the standard deviation be?

A) 4.33
B) 6.92
C) 4.54
D) 10

Question 53

When calculating the population standard deviation, we use N - 1 in the denominator.

Question 54

Given the following set of scores X : 10, 12, 6, 8, 9, 11, 13, 13, 5, 0, 1 What is the value of ?

A) 4.54
B) 206
C) 1
D) 0

Question 55

The median and the 50th percentile rank score will always have the same value.

Question 56

The median is most affected by unbalanced extreme scores.

Question 57

Given the following set of scores X : 10, 12, 6, 8, 9, 11, 13, 13, 5, 0, 1 What is the median?

A) 8
B) 9
C) 10
D) 11

Question 58

In general, ΣX² = ( ΣX)²

Question 59

Consider a distribution with N = 100, = 50, and = 9875. If 10 new scores of 50 were added to the distribution, what would happen to the sum of squares?

A) the value would increase
B) the value would decrease
C) the value would remain unchanged
D) cannot be determined from information given

Question 60

Given the following set of scores X : 10, 12, 6, 8, 9, 11, 13, 13, 5, 0, 1 What is the range?

A) 0
B) 13
C) 1
D) 3.6

Question 61

The equation for standard deviation is the same regardless of whether the scores are of a sample or a population.

Question 62

For data that are not normally distributed, the standard deviation will sometimes be negative.

Question 63

We use N - 1 in the denominator of the equation for calculating the sample standard deviation because it provides us with an accurate estimate of the population standard deviation.

Question 64

Variability and dispersion mean the same thing.

Question 65

Central tendency describes the central location of the set of scores.

Question 66

If the distribution contains unbalanced extreme scores, the mean is a better descriptor than the median.

Question 67

The variance is the square root of the standard deviation.

Question 68

The median is less subject to sampling variation than the mean.

Question 69

The mean is more often used for inference than the median.

Question 70

The mean is the arithmetic average of the scores.

Question 71

In a skewed distribution, the mean and median are equal.

Question 72

Central tendency and variability are synonymous.

Question 73

A deviation score is the same thing as a raw score.

Question 74

With grouped scores, the mode is the mid-point of the interval with the highest frequency.

Question 75

In a positively skewed distribution, the mean has a higher value than the median.

Question 76

The range is equal to the highest score minus the lowest score.

Question 77

Central tendency and variability are two terms that mean the same thing.

Question 78

The mean must have a value equal to one of the scores in the distribution.

Question 79

If the number of raw scores is odd, the median is always the score in the middle position.

Question 80

The mean is the same as the arithmetic average.