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