Deck 4: A: Numerical Descriptive Techniques

Question 1

The mean is affected by extreme values but the median is not.

Answer 1

True

Question 2

If the mean,median,and mode are all equal,the histogram must be symmetric and bell shaped.

Answer 2

True

Question 3

A data sample has a mean of 107,a median of 122,and a mode of 134.The distribution of the data is positively skewed.

Answer 3

False

Question 4

In a negatively skewed distribution,the mean is smaller than the median and the median is smaller than the mode.

Question 5

Which of the following statistics is a measure of central location?

A) The mean
B) The median
C) The mode
D) All of these choices are true.

Question 6

The median of an ordered data set with 30 items would be the average of the 15^th and the 16^th observations.

Question 7

$\sigma$ is a population parameter and $\bar { x }$ is a sample statistic.

Question 8

In a histogram,the proportion of the total area which must be to the left of the median is:

A) exactly 0.50.
B) less than 0.50 if the distribution is negatively skewed.
C) more than 0.50 if the distribution is positively skewed.
D) unknown.

Question 9

In a histogram,the proportion of the total area which must be to the right of the mean is exactly 0.50 if the distribution is symmetric and unimodal.

Question 10

Which of the following statements about the mean is not always correct?

A) The sum of the deviations from the mean is zero.
B) Half of the observations are on either side of the mean.
C) The mean is a measure of the central location.
D) The value of the mean times the number of observations equals the sum of all observations.

Question 11

Which of the following statements is true for the following observations: 9,8,7,9,6,11,and 13?

A) The mean,median,and mode are all equal.
B) Only the mean and median are equal.
C) Only the mean and mode are equal
D) Only the median and mode are equal.

Question 12

Lily has been keeping track of what she spends to eat out.The last week's expenditures for meals eaten out were $5.69,$5.95,$6.19,$10.91,$7.49,$14.53,and $7.66.The mean amount Lily spends on meals is $8.35.

Question 13

In a histogram,the proportion of the total area which must be to the left of the median is more than 0.50 if the distribution is positively skewed.

Question 14

The value of the mean times the number of observations equals the sum of the observations.

Question 15

In a histogram,the proportion of the total area which must be to the left of the median is less than 0.50 if the distribution is negatively skewed.

Question 16

The median of a set of data is more representative than the mean when the mean is larger than most of the observations.

Question 17

The mean is a measure of variability.

Question 18

In a bell shaped distribution,there is no difference in the values of the mean,median,and mode.

Question 19

Which measure(s)of central location is/are meaningful when the data are ordinal?

A) The mean and median
B) The mean and mode
C) The median and mode
D) Only mean

Question 20

Suppose a sample of size 50 has a sample mean of 20.In this case,the sum of all observations in the sample is 1,000.

Question 21

Which of the following statements about the median is not true?

A) It is more affected by extreme values than the mean.
B) It is a measure of central location.
C) It is equal to Q₂.
D) It is equal to the mode in a bell shaped distribution.

Question 22

Which of these measures of central location is not sensitive to extreme values?

A) The mean
B) The median
C) The mode
D) All of these choices are true.

Question 23

The sample mean is denoted by ____________________ and the population mean is denoted by ____________________.

Question 24

If a data set contains an even number of observations,the median is found by taking the ____________________ of these two numbers.

Question 25

The ____________________ mean of n returns (or growth rates)is the appropriate mean to calculate if you wish to estimate the mean rate of return (or growth rate)for any single period in the future.

Question 26

Which measure of central location can be used for both interval and nominal variables?

A) The mean
B) The median
C) The mode
D) All of these choices are true.

Question 27

The size of a sample is denoted by the letter ____________________ and the size of a population is denoted by the letter ____________________.

Question 28

Which of the following summary measures is sensitive to extreme values?

A) The median
B) The interquartile range
C) The mean
D) The first quartile

Question 29

Strip Mall Rent
Monthly rent data in dollars for a sample of 10 stores in a small town in South Dakota are as follows: 220,216,220,205,210,240,195,235,204,and 250.
{Strip Mall Rent Narrative} Compute the sample monthly average rent.

Question 30

The ____________________ is the least desirable of all the measures of central location.

Question 31

In a positively skewed distribution:

A) the median equals the mean.
B) the median is less than the mean.
C) the median is larger than the mean.
D) the mean can be larger or smaller than the median.

Question 32

Another word for the mean of a data set is the ____________________.

Question 33

Which of the following statements is true?

A) When the distribution is positively skewed,mean < median < mode.
B) When the distribution is negatively skewed,mean > median > mode.
C) When the distribution is symmetric and unimodal,mean = median = mode.
D) When the distribution is symmetric and bimodal,mean = median = mode.

Question 34

The ____________________ is not as sensitive to extreme values as the ____________________.

Question 35

The ____________________ is calculated by finding the middle of the data set,when the data are ordered from smallest to largest.

Question 36

In a perfectly symmetric bell shaped "normal" distribution:

A) the mean equals the median.
B) the median equals the mode.
C) the mean equals the mode.
D) All of these choices are true.

Question 37

If a data set is composed of 5 different numbers,there are ____________________ modes.

Question 38

There are three measures of central location;the mean,the ____________________,and the ____________________.

Question 39

In a histogram,the proportion of the total area which must be to the right of the mean is:

A) less than 0.50 if the distribution is negatively skewed.
B) exactly 0.50.
C) more than 0.50 if the distribution is positively skewed.
D) exactly 0.50 if the distribution is symmetric and unimodal.

Question 40

The ____________________ mean is used whenever we wish to find the "average" growth rate,or rate of change,in a variable over time.

Question 41

Hours Worked per Week
The following data represent the hours worked per week of a sample of 25 employees from a government department: 31,43,56,23,49,42,33,61,44,28,48,38,44,35,40,64,52,42,47,39,53,27,36,35,and 20.
{Hours Worked per Week Narrative} Compare the mean and median hours for these employees and use them to discuss the shape of the distribution.

Question 42

Computers
The following data represent the number of computers owned by a sample of 10 families from Chicago: 4,2,1,1,5,3,0,1,0,and 2.
{Computers Narrative} Is the distribution of the number of computers symmetric or skewed? Why?

Question 43

Salaries of Employees
The following data represent the yearly salaries (in thousands of dollars)of a sample of 13 employees of a firm: 26.5,23.5,29.7,24.8,21.1,24.3,20.4,22.7,27.2,23.7,24.1,24.8,and 28.2.
{Salaries of Employees Narrative} Compute the median salary.

Question 44

Computers
The following data represent the number of computers owned by a sample of 10 families from Chicago: 4,2,1,1,5,3,0,1,0,and 2.
{Computers Narrative} Compute the mean number of computers.

Question 45

Weights of Workers
The following data represent the number of employees of a sample of 25 companies: 164,148,137,157,173,156,177,172,169,165,145,168,163,162,174,152,156,168,154,151,174,146,134,140,and 171.
{Weights of Workers Narrative} Find the mean number of workers.

Question 46

Weights of Workers
The following data represent the number of employees of a sample of 25 companies: 164,148,137,157,173,156,177,172,169,165,145,168,163,162,174,152,156,168,154,151,174,146,134,140,and 171.
{Weights of Workers Narrative} Find the median number of workers.

Question 47

Weights of Workers
The following data represent the number of employees of a sample of 25 companies: 164,148,137,157,173,156,177,172,169,165,145,168,163,162,174,152,156,168,154,151,174,146,134,140,and 171.
{Weights of Workers Narrative} Is the distribution of the number of workers symmetric or skewed? Why?

Question 48

{Strip Mall Rent Narrative} What is the mode?

Question 49

Salaries of Employees
The following data represent the yearly salaries (in thousands of dollars)of a sample of 13 employees of a firm: 26.5,23.5,29.7,24.8,21.1,24.3,20.4,22.7,27.2,23.7,24.1,24.8,and 28.2.
{Salaries of Employees Narrative} Compare the mean salary with the median salary and use them to describe the shape of the distribution.

Question 50

Hours Worked per Week
The following data represent the hours worked per week of a sample of 25 employees from a government department: 31,43,56,23,49,42,33,61,44,28,48,38,44,35,40,64,52,42,47,39,53,27,36,35,and 20.
{Hours Worked per Week Narrative} Find the median hours.

Question 51

Hours Worked per Week
The following data represent the hours worked per week of a sample of 25 employees from a government department: 31,43,56,23,49,42,33,61,44,28,48,38,44,35,40,64,52,42,47,39,53,27,36,35,and 20.
{Hours Worked per Week Narrative} Compute the sample mean hours.

Question 52

Hours Worked per Week
The following data represent the hours worked per week of a sample of 25 employees from a government department: 31,43,56,23,49,42,33,61,44,28,48,38,44,35,40,64,52,42,47,39,53,27,36,35,and 20.
{Hours Worked per Week Narrative} Find the modal hours.

Question 53

Weights of Workers
The following data represent the number of employees of a sample of 25 companies: 164,148,137,157,173,156,177,172,169,165,145,168,163,162,174,152,156,168,154,151,174,146,134,140,and 171.
{Weights of Workers Narrative} Construct a stem and leaf display for the number of workers.

Question 54

{Strip Mall Rent Narrative} Compute the sample median.

Question 55

Pets Survey
A sample of 36 families were asked how many pets they owned.Their responses are summarized in the following table.

{Pets Survey Narrative} Explain what the mean,median,and mode tell you about this particular data set.

Question 56

Hours Worked per Week
The following data represent the hours worked per week of a sample of 25 employees from a government department: 31,43,56,23,49,42,33,61,44,28,48,38,44,35,40,64,52,42,47,39,53,27,36,35,and 20.
{Hours Worked per Week Narrative} Construct a stem and leaf display for the hours.

Question 57

Pets Survey
A sample of 36 families were asked how many pets they owned.Their responses are summarized in the following table.
$$\begin{array} { | l | l l l l l l | } \hline \text { Number of Pets } & 0 & 1 & 2 & 3 & 4 & 5 \\\hline \text { Number of Families } & 3 & 20 & 5 & 4 & 2 & 2 \\\hline\end{array}$$

-{Pets Survey Narrative} Determine the mean,the median,and the mode of the number of pets owned per family.

Question 58

Weights of Workers
The following data represent the number of employees of a sample of 25 companies: 164,148,137,157,173,156,177,172,169,165,145,168,163,162,174,152,156,168,154,151,174,146,134,140,and 171.
The number of hours a college student spent studying during the final exam week was recorded as follows: 7,6,4,9,8,5,and 10.Compute for the data and the value in an appropriate unit.

Question 59

Computers
The following data represent the number of computers owned by a sample of 10 families from Chicago: 4,2,1,1,5,3,0,1,0,and 2.
{Computers Narrative} Compute the median number of computers.

Question 60

Salaries of Employees
The following data represent the yearly salaries (in thousands of dollars)of a sample of 13 employees of a firm: 26.5,23.5,29.7,24.8,21.1,24.3,20.4,22.7,27.2,23.7,24.1,24.8,and 28.2.
{Salaries of Employees Narrative} Compute the mean salary.

Question 61

Ages of Senior Citizens
A sociologist recently conducted a survey of citizens over 65 years of age whose net worth is too high to qualify for Medicaid and who have no private health insurance.The ages of 22 uninsured senior citizens were as follows: 65,66,67,68,69,70,71,73,74,75,76,77,78,79,80,81,86,87,91,92,94,and 97.
{Ages of Senior Citizens Narrative} Calculate the median age of the uninsured senior citizens.

Question 62

Chebysheff's Theorem states that the percentage of observations in a data set that should fall within five standard deviations of their mean is at least 96%.

Question 63

2-Year Investment
Suppose you make a 2-year investment of $5,000 and it grows by 100% to $10,000 during the first year.During the second year,however,the investment suffers a 50% loss,from $10,000 back to $5,000.
{2-Year Investment Narrative} Calculate the geometric mean.

Question 64

The difference between the largest and smallest observations in an ordered data set is called the range.

Question 65

While Chebysheff's Theorem applies to any distribution,regardless of shape,the Empirical Rule applies only to distributions that are bell shaped.

Question 66

The data set 10,20,30 has the same variance as the data set 100,200,300.

Question 67

The mean of a sample of 15 measurements is 35.6 feet.Suppose that the sample is enlarged to 16 measurements,by including one additional measurement having a value of 42 feet.Find the mean of the sample of the 16 measurements.

Question 68

Ages of Senior Citizens
A sociologist recently conducted a survey of citizens over 65 years of age whose net worth is too high to qualify for Medicaid and who have no private health insurance.The ages of 22 uninsured senior citizens were as follows: 65,66,67,68,69,70,71,73,74,75,76,77,78,79,80,81,86,87,91,92,94,and 97.
{Ages of Senior Citizens Narrative} Explain why there is no mode for this data set.

Question 69

$\sigma$ is a population parameter and s is a sample statistic.

Question 70

According to Chebysheff's Theorem,at least 93.75% of observations should fall within 4 standard deviations of the mean.

Question 71

The value of the standard deviation may be either positive or negative,while the value of the variance will always be positive.

Question 72

2-Year Investment
Suppose you make a 2-year investment of $5,000 and it grows by 100% to $10,000 during the first year.During the second year,however,the investment suffers a 50% loss,from $10,000 back to $5,000.
{2-Year Investment Narrative} Compare the values of the arithmetic and geometric means.

Question 73

Suppose that a firm's sales were $3,750,000 five years ago and are $5,250,000 today.What was the geometric mean growth rate in sales over the past five years?

Question 74

A sample of 12 construction workers has a mean age of 25 years.Suppose that the sample is enlarged to 14 construction workers,by including two additional workers having common age of 25 each.Find the mean of the sample of 14 workers.

Question 75

2-Year Investment
Suppose you make a 2-year investment of $5,000 and it grows by 100% to $10,000 during the first year.During the second year,however,the investment suffers a 50% loss,from $10,000 back to $5,000.
{2-Year Investment Narrative} Calculate the arithmetic mean.

Question 76

Suppose that a firm's sales were $2,500,000 four years ago,and sales have grown annually by 25%,15%,-5%,and 10% since that time.What was the geometric mean growth rate in sales over the past four years?

Question 77

The standard deviation is expressed in terms of the original units of measurement but the variance is not.

Question 78

A mutual fund you purchased in the years 2011-2014 has the following rates of return shown below:
Compute the geometric mean.

Question 79

The mean of fifty sales receipts is $65.75 and the standard deviation is $10.55.Using Chebysheff's Theorem,75% of the sales receipts were between $44.65 and $86.85.

Question 80

Ages of Senior Citizens
A sociologist recently conducted a survey of citizens over 65 years of age whose net worth is too high to qualify for Medicaid and who have no private health insurance.The ages of 22 uninsured senior citizens were as follows: 65,66,67,68,69,70,71,73,74,75,76,77,78,79,80,81,86,87,91,92,94,and 97.
{Ages of Senior Citizens Narrative} Calculate the mean age of the uninsured senior citizens