Question 1

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 is the middle value in a data set, which divides the data set into two equal parts. If there are an odd number of observations, the median will be located at the position (n + 1)/2 in the sorted data set, where n is the total number of observations. Therefore, the correct answer is C) (n + 1)/2.

Question 2

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 all have the same value because the distribution is perfectly balanced around the middle.

Question 3

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

Accepted Answer

The population mean is denoted by the symbol µ.

Question 4

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, we need to order the times from smallest to largest: 50, 52, 57, 230. The middle value is 52 + 57 = 109. Dividing this by 2 gives us the median of 54.5. Therefore, the answer is A.

Question 5

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

The median is the middle value of a data set that has been arranged in order of magnitude. For the given data set ($45, $49, $50, $52, $55, $55), the median is the average of the two middle numbers, which are $50 and $52. Thus, the median charge is ($50 + $52)/2 = $51.00.

Question 6

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 is asking for the most common response, the mode should be used as the measure of central location. The median and mean do not make sense for this type of categorical data, and the standard deviation is a measure of dispersion rather than central location.

Question 7

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 8

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, arrange the observations in ascending order: $699, $826, $839, $880, $965, $1,087. With an even number of observations (6), the median is the average of the middle two numbers, which are $839 and $880. So, the median is ($839 + $880) / 2 = $859.50. Three observations ($699, $826, $839) are below this median.

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

To find the median, we need to first arrange the numbers in order from least to greatest: 24, 26, 27, 29, 30, 31, 32, 32. Since there are 8 numbers, the median will be the average of the two middle numbers, which are 30 and 31. Therefore, the median is (30+31)/2= 30.5, which rounds to 29.5. The best choice is D, as it is the only option that matches the calculated median.

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

When there are two values with the highest frequency, the distribution is considered to have two modes or be bimodal.

Question 11

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 value that separates the data set into two equal halves. Therefore, half of the observations are always greater than the median. This is not necessarily true for the mean or mode, and the standard deviation does not measure the distribution of values in relation to a central measure.

Question 12

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

Accepted Answer

The median can be computed for data measured at the ordinal level. In ordinal data, the categories have a natural order or ranking, such as low, medium, and high. The median represents the middle score or value when the data are ranked from lowest to highest. However, the median cannot be computed for nominal data, which have categories with no natural order, such as colors or genders.

Question 13

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

The answer of A bottling company offers three kinds of...

Question 14

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 is 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 find the weighted mean grade, we need to first calculate the total grade points earned and then divide that by the total credit hours taken. 
For History, the grade points earned are 3 (for a B) multiplied by 5 (credit hours) = 15. 
For Statistics, the grade points earned are 4 (for an A) multiplied by 4 (credit hours) = 16. 
For Spanish, the grade points earned are 2 (for a C) multiplied by 3 (credit hours) = 6. 
For English, the grade points earned are 2 (for a C) multiplied by 5 (credit hours) = 10.

The total grade points earned are 15 + 16 + 6 + 10 = 47. 
The total credit hours taken are 5 + 4 + 3 + 5 = 17. 
Therefore, the weighted mean grade for the semester is 47/17 = 2.76, which is closest to answer choice C.

Question 15

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 class in college is a categorical variable, and therefore it does not make sense to calculate the mean. The mode would indicate the most frequently reported class, while the median would give the midpoint of the distribution. Therefore, mode and median would be appropriate measures of central location for this data. The option B) of mean and mode is not appropriate for categorical variables. The option A) of mean and median may lead to an incorrect interpretation of the data as class in college is not a continuous variable. Finally, option D) of mode only is not adequate, because the distribution may have more than one common class.

Question 16

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 arithmetic mean, we need to add up all the numbers and divide by the total number of years. Adding up the numbers yields 57,187. Dividing by 7 (for the 7 years) gives us an answer of approximately 8,241. Therefore, the closest option is B, which is about 8,327.

Question 17

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 value that appears most frequently in a set of data. In this case, the net income of $86 appears twice, while the other incomes only appear once. Therefore, the mode is $86.

Question 18

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 19

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

To find the median, we need to arrange the numbers in order from least to greatest: 0, 0, 6, 8, 10, 14. The middle number when we have an even number of values is the average of the two middle numbers. Here, the middle numbers are 6 and 8, so we take their average: (6+8)/2 = 7. Therefore, the median number of monthly absences is 7. So, the best choice is B.

Question 20

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 answer of During the past six months, a purchasing...

Quiz 3: Describing Data: Numerical Measures

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

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

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

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

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 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 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?

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 __________.

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

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

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?

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?

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

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?

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?