1 |
The data in a random sample of n = 6 is shown below. Compute the mean and then fill in the deviations column. |
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x |
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Deviation from the mean |
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19 |
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54 |
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15 |
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50 |
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28 |
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32 |
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The sum of deviations is. |
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a |
0 |
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b |
5 |
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c |
10 |
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d |
76 |
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2 |
In the previous question, the sum of squared deviations is: |
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a |
1264 |
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b |
1268 |
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c |
1272 |
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d |
1276 |
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3 |
In the previous question, the mean squared deviation for the sample data is: |
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a |
250.8 |
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b |
255.2 |
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c |
258.8 |
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d |
262.4 |
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4 |
The variance of the data used for the previous three questions is: |
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a |
212.7 |
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b |
219.2 |
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c |
233.7 |
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d |
255.2 |
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5 |
The mean |
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a |
balances the number of observations on either side of mean value. |
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b |
is always the central (or middle) data point. |
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c |
is the center of gravity of the data. |
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d |
balances the deviations of the data from the mean. |
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e |
Both (c) and (d) are correct. |
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6 |
The following data is the grade point average (GPA) of five randomly selected E270 students. |
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x |
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3.2 |
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2.8 |
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2.5 |
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3.6 |
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3.8 |
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The variance of the sample is _______. |
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a |
0.210 |
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b |
0.234 |
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c |
0.292 |
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d |
0.321 |
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7 |
Treat the set below as population data: |
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x |
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114 |
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84 |
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152 |
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195 |
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105 |
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85 |
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The standard deviation is ________. |
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a |
39.57 |
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b |
41.55 |
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c |
43.62 |
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d |
45.80 |
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Tom delivers packages for UPS. His daily mileage for a random sample of 10 days is as follows. |
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x |
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42 |
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51 |
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32 |
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31 |
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58 |
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54 |
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62 |
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43 |
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38 |
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54 |
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8 |
The average daily miles Tom travels to deliver packages is ______. |
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a |
44.5 |
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b |
46.5 |
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c |
48.5 |
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d |
50.5 |
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9 |
In the previous question, the sum of squared deviations of daily mileage is ________. |
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a |
979.7 |
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b |
1010.1 |
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c |
1060.5 |
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d |
1081.3 |
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10 |
Using Tom’s daily mileage sample data, on average, Tom’s daily mileage deviates from the mean mileage by ________ |
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a |
9.12 |
miles |
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b |
9.86 |
miles |
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c |
10.03 |
miles |
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d |
10.86 |
miles |
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11 |
The following data represents the starting salaries for a sample of 42 students who graduated in 2014 with a bachelor’s degree in accounting. Data are in thousands of dollars: |
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53.9 |
54.5 |
59.3 |
60.3 |
63.4 |
64.8 |
58.5 |
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55.5 |
68.4 |
57 |
68.8 |
62.7 |
50.4 |
48.3 |
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42 |
63.5 |
61.3 |
57.9 |
45.1 |
62.8 |
45.3 |
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49.1 |
41.1 |
53.9 |
40.5 |
49.8 |
44.1 |
61.1 |
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56.9 |
64.5 |
46.6 |
57.1 |
59.3 |
46.7 |
65.8 |
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67.1 |
40 |
60 |
62.2 |
63.6 |
52.2 |
57.6 |
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Use Excel to expedite your calculations. |
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Find the mean salary (x̅ = ______). Compute the sum of squares of the salary data (∑x² = _______). The numerator of the quotient to compute the variance of the salary data is: _______. |
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a |
∑x² = |
125,620.9 |
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Numerator of the variance quotient = |
2,775.20 |
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b |
∑x² = |
128,184.6 |
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Numerator of the variance quotient = |
2,469.92 |
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c |
∑x² = |
130,800.6 |
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Numerator of the variance quotient = |
2,257.56 |
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d |
∑x² = |
133,470.0 |
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Numerator of the variance quotient = |
2,775.20 |
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12 |
The annual salary of the staff in a state government agency are shown below. The first column shows the annual salary and the second column the frequency (the number of staff earning that salary). |
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Annual Salary |
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Frequency |
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$102,000 |
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1 |
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85,000 |
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2 |
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76,000 |
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4 |
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50,000 |
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10 |
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42,000 |
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20 |
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35,000 |
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8 |
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The mean salary of agency’s staff is: |
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a |
$48,800 |
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b |
$55,000 |
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c |
$63,200 |
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d |
$65,000 |
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13 |
John works in an appliance store. The following is a report of his sales effort in a given month. The report shows the price and the percent of total units sold at that price. What is the mean price of the items sold by John? |
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Percent of |
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total units |
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Item |
Price |
sold |
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A |
$1,200 |
0.05 |
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B |
1000 |
0.20 |
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C |
800 |
0.35 |
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D |
200 |
0.30 |
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E |
50 |
0.10 |
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a |
x̅ = |
$650 |
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b |
x̅ = |
$630 |
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c |
x̅ = |
$615 |
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d |
x̅ = |
$605 |
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14 |
The following shows an E270 student’s scores for different course requirements and the corresponding weights assigned by the professor to each category. The scores are from the scale of 100. |
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Requirement |
Score |
Weight |
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Homework |
90 |
15% |
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Attendance |
100 |
10% |
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Tests |
80 |
30% |
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Common Final |
70 |
45% |
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100% |
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The student’s mean score is: |
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a |
85 |
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b |
84 |
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c |
82 |
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d |
79 |
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The instructor in a Statistics for Business and Economics wants to determine the proportion of students in that class who are business majors. Let “1” stand for business major and “0” for other majors. |
The following is the distribution obtained from the official class roster. |
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1 |
1 |
0 |
1 |
1 |
0 |
1 |
1 |
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0 |
0 |
1 |
1 |
1 |
0 |
1 |
0 |
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1 |
1 |
1 |
0 |
1 |
1 |
1 |
1 |
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0 |
1 |
1 |
0 |
1 |
1 |
0 |
1 |
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1 |
0 |
1 |
1 |
1 |
0 |
1 |
1 |
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1 |
1 |
0 |
1 |
0 |
1 |
1 |
0 |
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0 |
0 |
1 |
1 |
1 |
0 |
1 |
1 |
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15 |
The proportion of students who are business majors is ________. |
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a |
π = |
0.7321 |
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b |
π = |
0.7143 |
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c |
π = |
0.6964 |
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d |
π = |
0.6786 |
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16 |
The variance of the above binary data is ________. |
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a |
0.1806 |
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b |
0.1985 |
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c |
0.2181 |
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d |
0.2356 |
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17 |
A sample data set has n = 50 observations. The mean of the data x̅ = 46.5. The sum of squares ∑x² = 127793. The standard deviation of the data is ______. |
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a |
24.25 |
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b |
22.05 |
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c |
20.04 |
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d |
18.04 |
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Consider the sample of size 5 with data values of |
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x |
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16 |
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12 |
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20 |
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10 |
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17 |
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18 |
Compute the z-scores for each of the five data values. Which of the following is the correct set of z-values? |
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a |
b |
c |
d |
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0.25 |
0.25 |
0.25 |
0.25 |
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-0.75 |
-0.75 |
-0.75 |
-0.75 |
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1.25 |
1.25 |
1.25 |
0.75 |
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-1.25 |
-1.25 |
-0.50 |
-0.75 |
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0.50 |
0.75 |
1.25 |
0.50 |
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19 |
The mean of the z-scores in a data set |
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a |
is always equal to zero |
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b |
is always equal to one. |
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c |
is greater than zero for data sets that have large outlying values. |
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d |
is zero only when the x-values are balanced around the mean of x. |
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20 |
The standard deviation of z-scores in a data set |
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a |
is always equal to zero |
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b |
is always equal to one. |
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c |
is one only when the x-values are balanced around the mean of x. |
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d |
is greater than one for data sets that have large outlying values. |