Question 1

A sample of single persons receiving Social Security payments revealed these monthly benefits: $826, $699, $1,087, $880, $839, and $965. How many observations are below the median?
A)1
B)2
C)3
D)3.5

Accepted Answer

To find the median, first, we arrange the observations in ascending order: $699, $826, $839, $880, $965, $1,087. Since there are an even number of observations (6), the median is the average of the 3rd and 4th observations: ($839 + $880)/2 = $859.50. Therefore, 3 observations are below the median.

Question 2

Over the last six months, the following numbers of absences have been reported: 6, 0, 10, 14, 8, and 0. What is the median number of monthly absences?
A)6
B)7
C)8
D)3

Accepted Answer

The answer of Over the last six months, the following...

Question 3

During the past six months, a purchasing agent placed the following three orders for coal:  What is the weighted arithmetic mean price per ton?
A)$87.25
B)$72.33
C)$68.47
D)$89.18

Accepted Answer

The order can be separated into 3 parts:

- Order 1: 11eaaa24_e08a_aa83_86f9_21414fdf354f_T, price per ton = $80.50, quantity = 40 tons 
- Order 2: B4677_00, price per ton = $75.20, quantity = 60 tons 
- Order 3: TB4677_00, price per ton = $70.40, quantity = 20 tons

To find the weighted arithmetic mean price per ton, we need to calculate the total cost of all the orders and divide by the total quantity of coal purchased:

Total cost = ($80.50 x 40) + ($75.20 x 60) + ($70.40 x 20) = $3,760

Total quantity = 40 + 60 + 20 = 120 tons

Weighted arithmetic mean price per ton = Total cost / Total quantity = $3,760 / 120 = $31.33

Therefore, the answer is B) $72.33.

Question 4

A bottling company offers three kinds of delivery service: instant, same day, and within five days. The profit per delivery varies according to the kind of delivery. The profit for an instant delivery is less than the other kinds because the driver has to go directly to a grocery store with a small load and return to the bottling plant. To find out what effect each type of delivery has on the profit picture, the company summarized the data in the following table based on deliveries for the previous quarter.  What is the weighted mean profit per delivery?
A)$72
B)$110
C)$142
D)$97

Accepted Answer

To calculate the weighted mean profit per delivery, we need to use the formula:
(sum of (profit per delivery x number of deliveries))/(total number of deliveries)
Using the data from the table:

(40 x 200 + 120 x 400 + 150 x 600)/1200 = $97

Therefore, the weighted mean profit per delivery is $97.

As for the best choice(s), it depends on the company's priorities. If the company wants to maximize profit, then they should choose the delivery service with the highest profit per delivery, which is same day. However, if the company wants to balance profit and customer satisfaction, then offering all three delivery services could be the best option as it provides options to cater to different customer needs.

Question 5

A survey item asked students to indicate their class in college: freshman, sophomore, junior, or senior. Which measure(s) of central location would be appropriate for the data generated by that questionnaire item?
A)Mean and median
B)Mean and mode
C)Mode and median
D)Mode only

Accepted Answer

The data generated by the questionnaire item is ordinal, as it involves categories that have a natural order (freshman, sophomore, junior, senior) but not precise numerical differences between them. For ordinal data, the mode and median are appropriate measures of central location, as they can represent the most common category and the middle point of the data set, respectively. The mean is not suitable because it implies numerical values that can be averaged, which does not apply to ordinal categories.

Question 6

A sample of the paramedical fees charged by clinics revealed these amounts: $55, $49, $50, $45, $52, and $55. What is the median charge?
A)$47.50
B)$51.00
C)$52.00
D)$55.00

Accepted Answer

To find the median, first, arrange the charges in ascending order: $45, $49, $50, $52, $55, $55. Since there are an even number of charges (6), the median is the average of the middle two charges, which are $50 and $52. Thus, the median charge is ($50 + $52) / 2 = $102 / 2 = $51.00.

Question 7

Which one of the following is referred to as the population mean?
A)µ
B)s
C)σ
D)χ

Accepted Answer

The symbol µ represents the population mean.

Question 8

On a finance exam, 15 accounting majors had an average grade of 90. On the same exam, 7 marketing majors averaged 85, and 10 finance majors averaged 93. What is the weighted mean for all 32 students taking the exam?
A)89.84
B)89.33
C)89.48
D)10.67

Accepted Answer

The answer of On a finance exam, 15 accounting majors...

Question 9

What is the median of 26, 30, 24, 32, 32, 31, 27, and 29?
A)32
B)29
C)30
D)29.5

Accepted Answer

The median is the middle number when the numbers are arranged in order. First, we arrange the numbers in increasing order: 24, 26, 27, 29, 30, 31, 32, 32. The middle two numbers are 30 and 31. To find the median, we take the average of these two numbers: (30+31)/2 = 61/2 = 30.5, which is closest to 29.5. Therefore, the answer is D.

Question 10

Sometimes, a data set has two values that have the highest and equal frequencies. In this case, the distribution of the data can best be described as __________.
A)Symmetric
B)Bimodal (having two modes)
C)Positively skewed
D)Negatively skewed

Accepted Answer

If two values have the highest and equal frequencies, then there are two modes, which would result in a bimodal distribution.

Question 11

What is the relationship among the mean, median, and mode in a symmetric distribution?
A)They are all equal.
B)The mean is always the smallest value.
C)The mean is always the largest value.
D)The mode is the largest value.

Accepted Answer

In a symmetric distribution, the mean, median, and mode will all be equal.

Question 12

Assume a student received the following grades for the semester: History, B; Statistics, A; Spanish, C; and English,C. History and English are 5 credit-hour courses, Statistics a 4 credit-hour course, and Spanish a 3 credit-hour course. If 4 grade points are assigned for an A, 3 for a B, and 2 for a C, what is the weighted mean grade for the semester?
A)4.00
B)1.96
C)2.76
D)3.01

Accepted Answer

To calculate the weighted mean, we need to first calculate the total number of grade points earned by the student.

For History, the number of grade points earned = 3 (B grade) x 5 (credit hours) = 15
For Statistics, the number of grade points earned = 4 (A grade) x 4 (credit hours) = 16
For Spanish, the number of grade points earned = 2 (C grade) x 3 (credit hours) = 6
For English, the number of grade points earned = 2 (C grade) x 5 (credit hours) = 10

The total number of grade points earned = 15 + 16 + 6 + 10 = 47

The total number of credit hours for the semester = 5 + 4 + 3 + 5 = 17

The weighted mean grade for the semester = Total number of grade points earned / Total number of credit hours = 47/17 = 2.76

Therefore, the best choice is C, with the weighted mean grade for the semester being 2.76.

Question 13

The net incomes (in $millions) of a sample of steel fabricators are $86, $67, $86, and $85. What is the modal net income?
A)$67
B)$85
C)$85.5
D)$86

Accepted Answer

The mode is the most frequently occurring value in a set of data. In this case, the net income of $86 occurs twice, while the net incomes of $67 and $85 each occur once. Therefore, the mode is $86.

Question 14

For a data set with an odd number of observations that have been sorted from smallest to largest values, where is the median located?
A)n
B)n/2
C)(n + 1)/2
D)n + ½

Accepted Answer

The median of a sorted data set with an odd number of observations is located in the middle, which is (n + 1)/2.

Question 15

For a data set, half of the observations are always greater than the ____.
A)Median
B)Mode
C)Mean
D)Standard deviation

Accepted Answer

The median is the middle value of a data set, so half of the observations will be greater than it and half will be less than it. This is not necessarily true for the mean or mode, and standard deviation is a measure of how spread out the data is, not a specific value.

Question 16

What is the lowest level of measurement that a median can be computed?
A)Nominal
B)Ordinal
C)Interval
D)Ratio

Accepted Answer

A median can only be computed for ordinal, interval, and ratio level of measurements as they have a natural order to the variables. Among these, the lowest level of measurement for which a median can be computed is ordinal. In nominal level of measurement, there is no order to the variables, so a median cannot be computed.

Question 17

A stockbroker placed the following order for a customer: • 50 shares of Kaiser Aluminum at $104 a share
• 100 shares of GTE at $25.25 a share
• 20 shares of Boston Edison at $9.125 a share
What is the weighted arithmetic mean price per share?
A)$25.25
B)$79.75
C)$103.50
D)$46.51

Accepted Answer

The weighted arithmetic mean price per share is calculated by dividing the total cost of all shares by the total number of shares. For Kaiser Aluminum: 50 shares * $104 = $5200. For GTE: 100 shares * $25.25 = $2525. For Boston Edison: 20 shares * $9.125 = $182.5. Total cost = $5200 + $2525 + $182.5 = $7907.5. Total shares = 50 + 100 + 20 = 170. Weighted mean = $7907.5 / 170 = $46.51.

Question 18

The times (in minutes) that several underwriters took to review applications for similar insurance coverage are 50, 230, 52, and 57. What is the median length of time required to review an application?
A)54.5
B)141.0
C)97.25
D)109.0

Accepted Answer

To find the median, first arrange the times in ascending order: 50, 52, 57, 230. Since there is an even number of observations (4), the median is the average of the two middle numbers, which are 52 and 57. Thus, the median is (52 + 57) / 2 = 109 / 2 = 54.5 minutes.

Question 19

For the most recent seven years, the U.S. Department of Education reported the following number of bachelor's degrees awarded in computer science: 4,033; 5,652; 6,407; 7,201; 8,719; 11,154; 15,121. What is the annual arithmetic mean number of degrees awarded?
A)About 12,240
B)About 8,327
C)About 6,217
D)About 15,962

Accepted Answer

To find the annual arithmetic mean, we need to add up all the degrees awarded and divide by the number of years. Adding up the degrees gives us 4,033 + 5,652 + 6,407 + 7,201 + 8,719 + 11,154 + 15,121 = 58,287. Dividing by 7 (the number of years) gives us 8,327. Therefore, the answer is choice B, about 8,327 degrees awarded annually.

Question 20

A question in a market survey asks for a respondent's favorite car color. Which measure of central location should be used to summarize this question?
A)Mode
B)Median
C)Mean
D)Standard deviation

Accepted Answer

Since the question asks for respondents' favorite car color, which is a categorical variable, the mode should be used to summarize the data. The mode represents the most commonly chosen car color by the respondents. The median and mean are more appropriate for continuous numerical data, while the standard deviation is a measure of variability and not central location.

Quiz 3: Describing Data: Numerical Measures

A sample of single persons receiving Social Security payments revealed these monthly benefits: $826, $699, $1,087, $880, $839, and $965. How many observations are below the median?

Over the last six months, the following numbers of absences have been reported: 6, 0, 10, 14, 8, and 0. What is the median number of monthly absences?

During the past six months, a purchasing agent placed the following three orders for coal: What is the weighted arithmetic mean price per ton?

A survey item asked students to indicate their class in college: freshman, sophomore, junior, or senior. Which measure(s) of central location would be appropriate for the data generated by that questionnaire item?

A sample of the paramedical fees charged by clinics revealed these amounts: $55, $49, $50, $45, $52, and $55. What is the median charge?

Which one of the following is referred to as the population mean?

On a finance exam, 15 accounting majors had an average grade of 90. On the same exam, 7 marketing majors averaged 85, and 10 finance majors averaged 93. What is the weighted mean for all 32 students taking the exam?

What is the median of 26, 30, 24, 32, 32, 31, 27, and 29?

Sometimes, a data set has two values that have the highest and equal frequencies. In this case, the distribution of the data can best be described as __________.

What is the relationship among the mean, median, and mode in a symmetric distribution?

The net incomes (in $millions) of a sample of steel fabricators are $86, $67, $86, and $85. What is the modal net income?

For a data set with an odd number of observations that have been sorted from smallest to largest values, where is the median located?

For a data set, half of the observations are always greater than the ____.

What is the lowest level of measurement that a median can be computed?

A stockbroker placed the following order for a customer: • 50 shares of Kaiser Aluminum at $104 a share • 100 shares of GTE at $25.25 a share • 20 shares of Boston Edison at $9.125 a share What is the weighted arithmetic mean price per share?

The times (in minutes) that several underwriters took to review applications for similar insurance coverage are 50, 230, 52, and 57. What is the median length of time required to review an application?

For the most recent seven years, the U.S. Department of Education reported the following number of bachelor's degrees awarded in computer science: 4,033; 5,652; 6,407; 7,201; 8,719; 11,154; 15,121. What is the annual arithmetic mean number of degrees awarded?

A question in a market survey asks for a respondent's favorite car color. Which measure of central location should be used to summarize this question?