Question 1

A sample of 9 mothers was taken. The mothers were asked the age of their oldest child. You are given their responses below.  
a. Compute the mean.
b. Compute the variance.
c. Compute the standard deviation.
d. Compute the coefficient of variation.
e. Determine the 25th percentile.
f. Determine the median
g. Determine the 75th percentile.
h. Determine the range.

Accepted Answer

The answer of A sample of 9 mothers was taken....

Question 2

A set of visual displays that organizes and presents information that is used to monitor the performance of a company or organization in a manner that is easy to read, understand, and interpret is called a
A)stem-and-leaf display
B)stacked bar chart
C)data dashboard
D)crosstabulation

Accepted Answer

A data dashboard is a set of visual displays that organizes and presents information in a way that is easy to understand and interpret. It typically includes key performance indicators (KPIs) and metrics that allow companies and organizations to monitor their performance in real time and make data-driven decisions. A stem-and-leaf display, stacked bar chart, and crosstabulation are not typically used for this purpose.

Question 3

Chebyshev's theorem requires that z be
A)an integer
B)greater than 1
C)less than or equal to 3
D)between 0 and 4

Accepted Answer

Chebyshev's theorem states that at least (1 - 1/z^2) of the data values in any dataset will lie within z standard deviations from the mean, where z is any positive number greater than 1. Therefore, choice B, which states that z must be greater than 1, is the best choice.

Question 4

For the following data  Compute the following measures:
a. The mean
b. The variance
c. The standard deviation
d. The coefficient of variation
e. The 25th percentile
f. The median
g. The 75th percentile

Accepted Answer

The answer of For the following data  Compute the...

Question 5

Provide a five-number summary for the follow data.

Accepted Answer

The answer of Provide a five-number summary for the follow...

Question 6

The measure of central location most often reported for annual income and property value data is the
A)median
B)mode
C)weighted mean
D)aggregate mean

Accepted Answer

The median is the best measure of central location for annual income and property value data because these datasets often contain extreme values (outliers) that can significantly affect the mean, making it an unreliable measure. The median is not affected by outliers and gives a better representation of the "typical" value in a dataset. The mode is not useful for continuous numerical data like annual income and property values, and the weighted mean and aggregate mean are not necessary unless there is a specific reason to weight or aggregate the data.

Question 7

When the data are positively skewed, the mean will usually be
A)less than the median
B)greater than the median
C)less than the mode
D)greater than the mode

Accepted Answer

When a data set is positively skewed, it means that there are more extreme values on the right side of the distribution. This would pull the mean towards those higher values, making it greater than the median, which is simply the middle value in the data set. However, the mode (the most frequent value) may or may not be affected by skewness. Therefore, the best choice is B.

Question 8

The measure of location often used in analyzing growth rates in financial data is the
A)arithmetic mean
B)weighted mean
C)geometric mean
D)hyperbolic mean

Accepted Answer

The geometric mean is preferred for analyzing growth rates because it takes into account the changes in percentage terms rather than absolute terms. This is important for financial data where growth rates are usually expressed in percentage terms. The arithmetic mean is not a good choice because it can be heavily influenced by outliers and is not suitable for non-normal distributions. The weighted and hyperbolic means are rarely used in financial data analysis.

Question 9

A sample of 11 individuals shows the following monthly incomes.  
a.What would be a representative measure of central location for the above data? Explain.
b.Determine the mode.
c.Determine the median.
d.Determine the 60th percentile.
e.Drop the income of individual number 11 and compute the standard deviation for the first 10 individuals.

Accepted Answer

The answer of A sample of 11 individuals shows the...

Question 10

Chebyshev's theorem is applicable
A)only to large (n > 30) data sets
B)only to data sets with no outliers
C)only to bell-shaped data sets
D)to any data set

Accepted Answer

Chebyshev's theorem is applicable to any data set, regardless of the size, shape, or presence of outliers.

Question 11

The number of hours worked per week for a sample of ten students is shown below.  
a.Determine the median and explain its meaning.
b.Compute the 70th percentile and explain its meaning.
c.What is the mode of the above data? What does it signify?

Accepted Answer

The answer of The number of hours worked per week...

Question 12

The hourly wages of a sample of eight individuals is given below.  For the above sample, determine the following measures: 
a.The mean.
b.The standard deviation.
c.The 25th percentile.

Accepted Answer

The answer of The hourly wages of a sample of...

Question 13

A researcher has obtained the number of hours worked per week during the summer for a sample of fifteen students.  Using this data set, compute the
a. median
b. mean
c. mode
d. 40th percentile
e. range
f. sample variance
g. standard deviation

Accepted Answer

The answer of A researcher has obtained the number of...

Question 14

The following data show the yearly salaries of football coaches at some public high schools.  For the above sample, determine the following measures. 
a.The mean yearly salary
b.The standard deviation
c.The mode
d.The median
e.The 70th percentile

Accepted Answer

The answer of The following data show the yearly salaries...

Question 15

A private research organization studying families in various countries reported the following data for the amount of time 4-year old children spent alone with their fathers each day.  For the above sample, determine the following measures: 
a.The mean
b.The standard deviation
c.The mode
d.The 75th percentile

Accepted Answer

The answer of A private research organization studying families in...

Question 16

Suppose annual salaries for sales associates from a particular store have a mean of $32,500 and a standard deviation of $2,500.
a.Calculate and interpret the z-score for a sales associate who makes $36,000.
b.Use Chebyshev's theorem to calculate the percentage of sales associates with salaries between $26,250 and $38,750.
c.Suppose that the distribution of annual salaries for sales associates at this store is bell-shaped. Use the empirical rule to calculate the percentage of sales associates with salaries between $27,500 and $37,500.
d.Use the empirical rule to determine the percentage of sales associates with salaries less than $27,500.
e.Still suppose that the distribution of annual salaries for sales associates at this store is bell-shaped. A sales associate makes $42,000. Should this salary be considered an outlier? Explain.

Accepted Answer

The answer of Suppose annual salaries for sales associates from...

Question 17

A sample of twelve families was taken. Each family was asked how many times per week they dine in restaurants. Their responses are given below.  Using this data set, compute the
a. mode
b. median
c. mean
d. range
e. interquartile range
f. variance
g. standard deviation
h. coefficient of variation

Accepted Answer

The answer of A sample of twelve families was taken....

Question 18

The amount of time that a sample of students spends watching television per day is given below.  
a.Compute the mean.
b.Compute the median.
c.Compute the standard deviation.
d.Compute the 75th percentile.

Accepted Answer

The answer of The amount of time that a sample...

Question 19

In 2012, the average age of students at UTC was 22 with a standard deviation of 3.96. In 2013, the average age was 24 with a standard deviation of 4.08. In which year do the ages show a more dispersed distribution? Show your complete work and support your answer.

Accepted Answer

The answer of In 2012, the average age of students...

Question 20

For the following data  Compute the following measures:
a. The mean
b. The variance
c. The standard deviation
d. The coefficient of variation
e. The 25th percentile
f. The median
g. The 75th percentile

Accepted Answer

The answer of For the following data  Compute the...

Quiz 3: Descriptive Statistics: Numerical Measures

A set of visual displays that organizes and presents information that is used to monitor the performance of a company or organization in a manner that is easy to read, understand, and interpret is called a

Chebyshev's theorem requires that z be

For the following data Compute the following measures: a. The mean b. The variance c. The standard deviation d. The coefficient of variation e. The 25th percentile f. The median g. The 75th percentile

Provide a five-number summary for the follow data.

The measure of central location most often reported for annual income and property value data is the

When the data are positively skewed, the mean will usually be

The measure of location often used in analyzing growth rates in financial data is the

Chebyshev's theorem is applicable

The number of hours worked per week for a sample of ten students is shown below. a.Determine the median and explain its meaning. b.Compute the 70th percentile and explain its meaning. c.What is the mode of the above data? What does it signify?

The hourly wages of a sample of eight individuals is given below. For the above sample, determine the following measures: a.The mean. b.The standard deviation. c.The 25th percentile.

A researcher has obtained the number of hours worked per week during the summer for a sample of fifteen students. Using this data set, compute the a. median b. mean c. mode d. 40th percentile e. range f. sample variance g. standard deviation

The following data show the yearly salaries of football coaches at some public high schools. For the above sample, determine the following measures. a.The mean yearly salary b.The standard deviation c.The mode d.The median e.The 70th percentile

A sample of twelve families was taken. Each family was asked how many times per week they dine in restaurants. Their responses are given below. Using this data set, compute the a. mode b. median c. mean d. range e. interquartile range f. variance g. standard deviation h. coefficient of variation

The amount of time that a sample of students spends watching television per day is given below. a.Compute the mean. b.Compute the median. c.Compute the standard deviation. d.Compute the 75th percentile.

In 2012, the average age of students at UTC was 22 with a standard deviation of 3.96. In 2013, the average age was 24 with a standard deviation of 4.08. In which year do the ages show a more dispersed distribution? Show your complete work and support your answer.

For the following data Compute the following measures: a. The mean b. The variance c. The standard deviation d. The coefficient of variation e. The 25th percentile f. The median g. The 75th percentile