BUS 271 Chapter 3
The mode can be computed for which of the following levels of data?
Nominal, Ordinal, Interval, and Ratio
Why would one use a grouped mean or standard deviation?
Only the frequency distribution data is available.
What does N represent in the formula for the population variance?
The number of observations in the population
Which one of the following is a statistic?
the mean of a sample
What is the variance of the following sample data? 8, 6, 2, 8
8.00
Which of the following statements are reasons to study the dispersion of data? Select all that apply.
A small value for dispersion indicates that the data is closely clustered around the center. It allows us to compare the spread in two or more distributions.
The mean, median, and mode are all the same for which type of distribution?
A symmetrical distribution.
Which of the following would be calculated using the geometric mean? Select all that apply.
Average growth rate for four years of sales figures. Average percentage annual yield for a portfolio of stocks.
Which of the following averages would be calculated using the geometric mean?
The average annual rate of growth of undergraduate enrollment for the last 10 years. The average annual rate of return for a mutual fund held for five years.
Which of the following statements best describes the strength of the range as a measure of dispersion?
The calculation in easy to perform.
The formula for the weighted mean is Xw=Σ(wX)Σw Which of the following statements are true of the weighted mean? Select all that apply.
The denominator of the weighted mean is always the sum of the weights. It is used when there are several observations of the same value. It is a special case of the arithmetic mean.
How does the formula for the sample mean differ from the formula for population mean?
The formulas are functionally the same, but 'n' (the sample size) is used instead of 'N' (the population size).
Which one of the following is true for a symmetrical distribution?
The mean, median and mode all have the same value.
True or false: The standard deviation is a measure of dispersion.
True
The Population Mean is:
the arithmetic mean of all of the values in the population
Chebyshev's Theorem says that for any set of observations, the proportion of values that lie within kstandard deviations of the mean is:
1-1/k2 for k>1
Given the following population data sets, which has a smaller population variance?
12, 14, 15, 12, 14, 13
What is the variance of the following population data? 2, 0, 1, 9
12.50
The number of customers using a store's credit card has grown the last five years at the following rates: 12%, 20%, 31%, -5%, and 10%. Calculate the average annual growth rate (geometric mean).
12.97%
What is the variance of the following sample data? 2, 6, 2, 10
14.67
What is the standard deviation of the following sample data? 2, 6, 2, 0, 5
2.45
What is the standard deviation of the following population data? 3, 6, 2, 9
2.74
What is the standard deviation of the following sample data? 7, 6, 2, 0, 5
2.92
A house that sold for $340,000 in 2009 sold for $420,000 in 2016. What was the annual rate of increase of the price?
3.1%
What is the variance of the following population data? 2, 6, 1
4.67
Find the median for the following sample of data: 8, 4, 5, 13, 1, 8, 3.
5
Suppose a population is made up of the following values: 1, 8, 5, 6. What is the population mean?
5
Find the median for the following sample of data: 3, 2, 7, 5, 7, 6.
5.5
Find the median for the following sample of data: 8, 1, 6, 6, 4, 8, 2, 8, 20.
6
A stock has returns for four years of 5%, 17%, 64%, and -35%. Calculate the average annual rate of return (geometric mean).
6.98%
Calculate the mean of the following sample of data: 12, 4, 5.
7
What is the range for the following set of data? 3, 5, 4, 6, 7, 10, 9
7
A stock sold at $32 per share in 2006. By 2016 the price per share was $65. What was the annual rate of increase for the stock?
7.3%
Which one of the following is an unethical approach to reporting statistics?
Giving only the measures of location and dispersion that support your point of view.
Of the following, which one is an advantage of the standard deviation over the variance?
It is in the same units as the data.
Which of the following is an advantage of the mode?
It is not affected by extreme values.
Which of the following are advantages of the variance compared to the range? Check all that apply.
It is not unduly influenced by large or small values. It uses all of the values in the data, not just two.
Which of the following statements is true for a mean or standard deviation calculated for grouped data?
It is only an estimate of the corresponding actual value.
Which of the following is an advantage of the range compared to the variance? Check all that apply.
It is simpler to understand and calculate.
What does a measure of dispersion tell us about a set of data?
It tells us about the spread of the data.
Why is it important to consider measures of dispersion as well as measures of location when reporting statistics?
Measures of location do not tell us about the spread or clustering of data.
Which of the following statements describe weaknesses of the range as a measure of dispersion? Select all that apply.
Only two values from the data set are used. It may be unduly influenced by an especially small value. It may be unduly influenced by an unusually large value
In 2008 a share of Quintex Corp. stock was worth $44. In 2016 it was worth $68. Which of the following will best represent the average annual increase in value of the stock?
Rate of increase over time
Which of the following kinds of data can be used to find a median value?
Ratio level data Ordinal level data Interval level data
How do you find the Population Mean for a set of data?
Sum the values in the population and then divide by the number of values in the population.
Which of the following is a population parameter if you are investigating the average age of patients at a local hospital?
The ages of all of the patients at a local hospital.
What does n represent in the formula for the sample variance?
The sample size
What does s represent in the formula for the standard deviation of grouped data variance?
The sample standard deviation
Which statement is true with regard to differences in the formula for the population and samples variances?
The sample variance measures deviations from the sample mean, whereas the population variance uses the population mean.
Which of the following statements best defines the mode?
The value of the observation that appears most frequently
Given the following weights (in ounces) of four apples, 6, 8, 10, and 7, which of the following is true?
The variance would be in ounces-squared.
Which of the following are important properties of the arithmetic mean? Check all that apply.
There is only one mean for a set of data. Σ(X-X)=0 i.e. the sum of the deviations is zero. All of the values in the data are used in calculating the mean.
What is the purpose of a measure of location?
To indicate the center of a distribution of data.
Which of the following statements represent an ethical approach to the use of statistics? Check all that apply.
We must maintain an independent and principled point of view. A statistical report requires objective and honest communication of results.
What does a small value for a measure of dispersion tell us about a set of data?
What does a small value for a measure of dispersion tell us about a set of data?
What characteristic of a data set makes the median the better measure of the center of the data than the mean?
When the data set includes one or two very large or very small values.
Which of the following is the correct formula for the Mean of Grouped Data?
X=ΣfMn
A statistic is:
a characteristic of a sample
Chebyshev's Theorem states that the proportion of values is at least 1-1/k2. What is the meaning of k?
k is the number of standard deviations, greater than 1, within which that proportion of observations will be found.
For a positively skewed distribution, the ordering of the median, mode, and mean, from least to greatest, would be which one of the following?
mode, median, mean
Most of the used cars sold by a used car dealer are priced at about $16,000. The median price of a car on the lot is $14,450 but a few sell for under $2000. The distribution of car prices is:
negatively skewed
Which of the following is the correct formula for the standard deviation of grouped data?
s=√Σf(M−x)2n−1
Calculate the mean of the following sample of data: 12, 15, 6, 4, 8.
9
What is the range for the following set of data? 4, 12, 5, 3, 7, 8, 9
9
For which of the following variables can one calculate a median?
Daily temperatures in August for the past 10 years Finishing position in a marathon (1st, 2nd, 3rd, ...) Shoe size
What is the best measure of the center of an income distribution in a country where most of the households have annual incomes of about $40,000, but a small number of households have incomes above $1,000,000?
Median
Which of the following is true regarding medians and means?
Medians can be calculated from ordinal-level data, but means can't.
Which of the following is true regarding the application of Chebyshev's theorem and the Empirical Rule? Check all that apply.
Only Chebyshev's applies to skewed distributions. The Empirical Rule gives more precise answers for the symmetrical, bell-shaped distribution.
Which one of the following is true regarding the use of the mode, mean, and median for different levels of measurement?
Only the mode can be used for nominal-level data.
Choose the best definition for the variance.
The arithmetic average of the squared deviations from the mean.
Which of the following accurately describes the median of a set of data?
The midpoint of the data when it is arranged in order.
Which of the following are reasons why the mode would not be a good choice of measure for the describing the center of a set of data? Check all that apply.
The most frequent observation is much higher or much lower than most of the data values. No observation occurs more than once. The data is bimodal.
Why would the median be a better measure of the center than the mean for the following set of data? 3, 4, 4, 4, 5, 6, 7, 23
The number 23 is much larger than the other numbers and would unduly influence the mean.
Which of the following are used to measure dispersion? Check all that apply.
Variance Standard Deviation Range
When you calculate the sample mean, you divide the sum of the values in the sample by
the number of values in the sample.
Sample standard deviation is:
the square root of sample variance
The dispersion of a set of data is often referred to as which of the following?
variation or spread
What is the standard deviation of the following population data? 3, 1, 2, 9, 5
2.83
A mutual fund has a rate of return for five years of 10%, 14%, -20%, 18%, and 22%. Calculate the average rate of return (geometric mean). Round to the nearest tenth of a percent.
7.6%
According to Chebyshev's theorem, what proportion of values for a bimodal distribution will be found within two standard deviations of the mean?
75%
The average age of undergraduate students at Grand Canyon University is 44. If the standard deviation is 4, what percentage of undergraduate students are between 36 and 52 years old?
75%
Suppose the wait time at the emergency room follow a symmetrical, bell-shaped distribution with a mean of 90 minutes and a standard deviation of 10 minutes. What percentage of emergency room patients will wait between 1 hour and 2 hours?
99.7%
What is the definition of "parameter"?
A characteristic of a population.
What is another term for the "average" value of a distribution?
A measure of location
Which of the following is true regarding the application of Chebyshev's theorem and the Empirical Rule? Check all that apply.
Chebyshev's theorem works for symmetrical, bell-shaped distributions. Chebyshev's theorem applies to any set of values.
For which of the following variables can one calculate an arithmetic mean?
Daily temperatures in August for the past 10 years Time to run a marathon
Why is it important to consider all the measures of location in reporting statistics?
Each of the measures has advantages and disadvantages in representing the data.
True or false: It is appropriate to remove outliers in the data set to make the data easier to analyze.
False
True or false: The variance is a measure of central tendency.
False
Which of the following are disadvantages of the mode?
For many sets of data there is no mode. For many sets of data there are multiple modes.
Which statement best describes the difference between the formula for Population and Sample variance?
For the sample variance, dividing by n-1 corrects a tendency to underestimate population variance.
Most of the items sold at a garage sale cost about $12. Nothing sold for more than $15, but a few items cost only a few cents. What would be the best measure of the center of the distribution of sale prices?
Median
The median would be a better measure for the center of the data for of which of the following data sets?
{9, 11, 14, 16, 1, 12, 15, 17}
Choose the formula for the Sample Variance.
Σ(X−X)2n−1
Which of the following is the correct formula for the population variance?
Σ(X−μ)2N
In the formula for calculating the mean of grouped data, M stands for:
the midpoint of a given class
The median is defined as:
the midpoint of the values after they have been arranged in rank order
The larger the population variance is for a data set,
the more spread out the data is
