Question 1

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

Accepted Answer

The median is the value that separates the lower and upper halves of a data set. Therefore, half of the observations in the data set are always greater than the median. The mode is the most frequently occurring value and may not be a representative measure of central tendency in skewed or multimodal distributions. The mean and standard deviation are affected by outliers, and therefore, may not be representative of the data set.

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?

Accepted Answer

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

Question 3

A disadvantage of using an arithmetic mean to summarize a set of data is that ________.

Accepted Answer

The arithmetic mean is sensitive to outliers or extreme values in the data set. This means that one or two extremely small or large values can greatly affect the value of the mean, making it less representative of the overall data set. Therefore, using the arithmetic mean as a summary statistic can sometimes lead to misleading conclusions.

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?

Accepted Answer

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

Question 5

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

Accepted Answer

The median is the middle value in a sorted data set. For a data set with an odd number of observations, there will always be one middle value. The position of the middle value in the sorted data set can be found by dividing the total number of observations (n) by 2 and adding 1/2, which gives the formula (n + 1)/2. Therefore, the correct answer is C.

Question 6

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?

Accepted Answer

Since the list of times is already in numerical order, we can simply find the middle value. The median length of time is the middle value, which is 52. However, since there are an even number of values, we need to take the average of the two middle values, which are 52 and 57. 
(52+57)/2 = 54.5
Therefore, the median length of time required to review an application is 54.5 minutes.

Question 7

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?

Accepted Answer

Weighted mean = (15 * 90 + 7 * 85 + 10 * 93) / 32 = 89.84

Question 8

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

Accepted Answer

The given code "11ea71e6_5be8_78b7_91e5_ef4d4bb78783_TB2636_00" does not provide any useful information to solve the problem.

Without additional information, we cannot calculate the weighted arithmetic mean price per ton. Therefore, the correct answer choice is B) Not enough information provided.

Question 9

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?

Accepted Answer

Since the question asks for the favorite car color, it is categorical data and cannot be averaged. Therefore, the best measure of central location to summarize this question is the mode, which represents the most frequently chosen car color.

Question 10

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?

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 11

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

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 12

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

Accepted Answer

The symbol µ represents the population mean, which is the average value of a population.

Question 13

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

Accepted Answer

To find the median, we need to arrange the numbers in order from least to greatest: 24, 26, 27, 29, 30, 31, 32, 32. The middle number(s) is the median. Since we have an even number of values, we take the average of the two middle values, which are 29 and 30. The average of 29 and 30 is 29.5, so the median is 29.5. Therefore, the answer is D.

Question 14

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?

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 15

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

Accepted Answer

The median can only be computed for ordinal and higher levels of measurement. In nominal measurement, the data are simply labeled into categories with no order or hierarchy, so there is no meaningful way to calculate a median. The median can be calculated for ordinal data because there is a natural rank order among the categories. However, it is important to note that the median may not always be the best measure of central tendency for ordinal data, since it does not take into account the magnitude of differences between categories.

Question 16

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?

Accepted Answer

To calculate the weighted mean grade, we need to multiply the grade points by the credit hours for each course, add them together, and then divide by the total credit hours.

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

Total grade points = 15 + 16 + 6 + 10 = 47
Total credit hours = 5 + 4 + 3 + 5 = 17

Weighted mean grade = 47/17 = 2.76

Therefore, the answer is C.

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?

Accepted Answer

The mode is the value that appears most frequently in the set. In this case, the value of $86 appears twice, while $67 and $85 each appear once. Therefore, the modal net income is $86.

Question 18

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?

Accepted Answer

To find the annual arithmetic mean, we need to add up all the degrees and then divide by the number of years (which is 7 in this case). 
Adding up all the degrees: 
4,033 + 5,652 + 6,407 + 7,201 + 8,719 + 11,154 + 15,121 = 58,287 
Dividing by 7: 
58,287 / 7 = 8,327. 
Therefore, the annual arithmetic mean number of degrees awarded is about 8,327. 
The best choice is only B.

Question 19

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?

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 20

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 ________.

Accepted Answer

When a data set has two values that have the highest and equal frequencies, it indicates that there are two modes in the distribution, making it bimodal.

Quiz 3: Describing Data: Numerical Measures