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

Accepted Answer

When the mean is less than the median, the distribution is 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

Accepted Answer

Since the distribution is positively skewed, this means that there are a few professors with very high salaries that are pulling the mean up, making it greater than the median. Therefore, the mean is greater than the 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

Accepted Answer

To find the range, we need to subtract the smallest score from the largest score. The smallest score is 8 and the largest score is 20. Therefore, the range is 20 - 8 = 12. The best choice is B.

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

Accepted Answer

The mode is the value(s) that appears most frequently in a distribution. In this case, both 11 and 13 appear three times, which makes them modes. Therefore, the answer is C.

Question 5

The most commonly encountered measure of central tendency is the _________.
A) mean
B) median
C) mode
D) standard deviation

Accepted Answer

The mean is the most commonly used measure of central tendency and is calculated as the sum of all values in the data set divided by the number of values. It provides a representative average of the data set and is often used in statistical analysis and reporting. The median and mode are also measures of central tendency, but they are less commonly used in comparison to the mean. The standard deviation is a measure of dispersion, not central tendency.

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

Accepted Answer

To find the mean, we need to add up all the scores and divide by the total number of scores. Adding up the scores, we get 5+2+8+2+3+2+4+12 = 38. Dividing by the total number of scores (which is 8), we get 38/8 = 4.75. Therefore, the mean for this distribution is 4.75.

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

Accepted Answer

To find the standard deviation, we need to use the formula:

s = sqrt [ Σ(xi - x)^2 / (n - 1) ]

Where:
Σ = the sum of
xi = each individual score
x = the mean of all scores
n = the total number of scores

First, we need to find the mean:

x = (5 + 2 + 8 + 2 + 3 + 2 + 4 + 12) / 8 = 4.25

Next, we calculate the variance:

Σ(xi - x)^2 = (5 - 4.25)^2 + (2 - 4.25)^2 + (8 - 4.25)^2 + (2 - 4.25)^2 + (3 - 4.25)^2 + (2 - 4.25)^2 + (4 - 4.25)^2 + (12 - 4.25)^2
= 0.3025 + 5.7025 + 14.6025 + 5.7025 + 1.3225 + 5.7025 + 0.2025 + 51.5625
= 85.8200

s = sqrt [ 85.8200 / (8 - 1) ]
= sqrt [ 12.2600 ]
= 3.4997

Rounding to two decimal places, the standard deviation is approximately 3.58. Therefore, the best choice is D.

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

Accepted Answer

To find the median, first, arrange the scores in ascending order: 2, 2, 2, 3, 4, 5, 8, 12. Since there are 8 scores (an even number), the median is the average of the 4th and 5th scores: (3 + 4) / 2 = 3.5.

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

Accepted Answer

The overall mean weight is calculated by dividing the total weight of all team members by the total number of team members. For team A, the total weight is 15 * 140 = 2100 lbs. For team B, it's 7 * 135 = 945 lbs. For team C, it's 20 * 160 = 3200 lbs. The total weight for all teams is 2100 + 945 + 3200 = 6245 lbs. The total number of members is 15 + 7 + 20 = 42. Therefore, the overall mean weight is 6245 / 42 = 148.69 lbs.

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

Accepted Answer

If everyone gets the 10 point bonus, the total number of points earned by the class would increase by 10 points for each student. Since the class average is calculated by dividing the total number of points earned by the number of students, adding 10 points to each student's score would increase the class average by 10 points. Therefore, the class mean would equal 83 + 10 = 93, making choice C the correct answer.

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

Accepted Answer

1. Find the mean: (13+11+11+9+12+13+16+14+11+10+8+13+20) / 13 = 12
2. Subtract each score from the mean: -1, -1, -1, -3, 0, 1, 4, 2, -1, -2, -4, 1, 8
3. Square each result: 1, 1, 1, 9, 0, 1, 16, 4, 1, 4, 16, 1, 64
4. Find the sum of the squared differences: 118
5. Divide by the number of scores minus 1: 118 / 12 = 9.76

Question 12

For any distribution of scores Σ( X - µ ) = _________.
A) 0
B) Σ X
C) 1
D)

Accepted Answer

This is because the formula for calculating the sum of deviations from the mean (Σ(X - µ)) is designed in such a way that the deviations above the mean exactly cancel out the deviations below the mean, resulting in a net sum of 0.

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

Accepted Answer

To find the median, first, the scores need to be arranged in ascending order: 8, 9, 10, 11, 11, 11, 12, 13, 13, 13, 14, 16, 20. The median is the middle number, which is 12 in this case, since there are 13 scores.

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

Accepted Answer

To calculate the variance, we need to first find the mean:
Mean = (5 + 2 + 8 + 2 + 3 + 2 + 4 + 12)/8 = 4.25

Next, we find the deviation from the mean for each score:
(5-4.25), (2-4.25), (8-4.25), (2-4.25), (3-4.25), (2-4.25), (4-4.25), (12-4.25)
= 0.75, -2.25, 3.75, -2.25, -1.25, -2.25, -0.25, 7.75

Then, we square each deviation:
0.56, 5.06, 14.06, 5.06, 1.56, 5.06, 0.06, 60.06

To find the variance, we sum up these squared deviations and divide by n-1:
(0.56 + 5.06 + 14.06 + 5.06 + 1.56 + 5.06 + 0.06 + 60.06)/7
= 12.79

Therefore, the variance for this distribution is 12.79.

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

Accepted Answer

To find the mean, add all the scores together and then divide by the number of scores. The sum of the scores is 161, and there are 13 scores. 161 divided by 13 equals 12.38.

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

Accepted Answer

The answer of In a certain statistics course, four exams...

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

Accepted Answer

The standard deviation is calculated by finding the square root of the variance. First, find the mean (average) of the scores, then calculate the variance by finding the average of the squared differences from the Mean, and finally, take the square root of the variance to get the standard deviation. The calculation based on the given scores results in a standard deviation of approximately 3.12, making option A correct.

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

Accepted Answer

The answer of An industrial psychologist observed 8 drill-press operators...

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

Accepted Answer

The mode is the most frequent score in the distribution. In this case, the score of 2 appears three times, while all other scores appear only once or twice. Therefore, the mode for this distribution is 2.

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

Accepted Answer

The median is the best measure of central tendency for these scores because it is not affected by the extreme values (0.1 and 0.5), which would skew the mean significantly. The median provides a better representation of the central value of the dataset.

Quiz 4: Measures of Central Tendency and Variability

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

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 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 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) _________.

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

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 _________.

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 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.

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

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 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 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.

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?