Chapter 3
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%
What is the range for the following set of data? 4, 12, 5, 3, 7, 8, 9
9
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.
What does N represent in the formula for the population variance?
The number of observations in the population
What does n represent in the formula for the sample variance?
The number of observations in the sample
What does s represent in the formula for the standard deviation of grouped data variance?
The sample standard deviation
What is the purpose of a measure of location?
To indicate the center of a distribution of data.
What does a measure of dispersion tell us about a set of data?
The spread of data
Which one of the following is a statistic?
The mean of a sample
Which one of the following is true for a symmetrical distribution?
The mean, median and mode all have the same value.
The mean, median, and mode are all the same for which type of distribution?
The mean, median, and mode are all the same for which type of distribution?
Which of the following accurately describes the median of a set of data?
The midpoint of the data when it is arranged in order.
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).
True or false: The standard deviation is a measure of dispersion.
True
Which measure of dispersion results in units that are different from the data?
Variance
The median would be a better measure for the center for which of the following data sets?
{9, 11, 14, 16, 1, 12, 15, 17}
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.
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
The difference between the largest and the smallest values in a data set is called the ______.
Range
Which of the following are used to measure dispersion? Check all that apply.
Range, Variance, and Standard Deviation
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
The dispersion of a set of data is often referred to as which of the following?
variation or spread
Calculate the mean of the following sample of data: 12, 4, 6, 6.
7
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
Which of the following is the correct formula for the population variance?
E(X-U)2/N
Which of the following kinds of data can be used to find a median value?
Interval level data Ordinal level data Ratio level data
What does a small value for a measure of dispersion tell us about a set of data?
It indicates that the data is closely clustered around the center.
The formula for the weighted mean is XXw=Σ(wX)ΣwΣ(wX)Σw Which of the following statements are true of the weighted mean? Select all that appl
It is a special case of the arithmetic mean. 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.
Which of the following is an advantage of the mode?
It is not affected by extreme values.
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.
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.
Why would one use a grouped mean or standard deviation?
Only the frequency distribution data is available.
Choose the formula for the Sample Variance.
S2= E(X-XBar)2/N-1
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.
Choose the best definition for the variance.
The arithmetic average of the squared deviations from the mean.
Which of the following averages would be calculated using the geometric mean?
The average annual rate of return for a mutual fund held for five years. The average annual rate of growth of undergraduate enrollment for the last 10 years.
Which of the following statements best describes the strength of the range as a measure of dispersion?
The calculation is easy to perform.
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.
A statistic is:
a characteristic of a sample
Chebyshev's Theorem says that for any set of observations, the proportion of values that lie within k standard 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 population data? 3, 1, 2, 9, 5
2.83
What is the standard deviation of the following sample data? 7, 6, 2, 0, 5
2.92
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
Find the median for the following sample of data: 3, 2, 7, 5, 7, 6.
5.5
The Empirical rule states approximately what percentage of observations will be found within some deviation from the mean for a normal distribution. Match the percentage of observation to the range.
68% matches Choice plus or minus one standard deviation. 95% matches Choice plus or minus two standard deviations 99.7% matches Choice plus or minus three standard deviation
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%
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%
What is the variance of the following sample data? 8, 6, 2, 8
8
Calculate the mean of the following sample of data: 12, 15, 6, 4, 8.
9
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
True or false: The variance is a measure of central tendency.
False
For which of the following variables can one calculate a median?
Finishing position in a marathon (1st, 2nd, 3rd, ...) Daily temperatures in August for the past 10 years Shoe size
Which of the following are disadvantages of the mode?
For many sets of data there are multiple modes. For many sets of data there is no mode.
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.
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.
Which of the following are advantages of the variance compared to the range? Check all that apply.
It uses all of the values in the data, not just two. It is not unduly influenced by large or small values.
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.
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
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 apples squared
Which one of the following is true for a negatively skewed distribution?
There are a small number of observations that are much lower in value than most of the data.
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. All of the values in the data are used in calculating the mean. Σ(X-XX)=0 i.e. the sum of the deviations is zero.
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.
In a certain neighborhood most of the houses cost about $60,000. One house cost $700,000 and the mean cost was $82,500. The distribution of housing costs is:
positively skewed
The Population Mean is:
the arithmetic mean of all the values in a population
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
When you calculate the sample mean, you divide the sum of the values in the sample by
the number of values in the sample.
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 with data that has repeated values, such as a frequency distribution.
Which of the following is true regarding the application of Chebyshev's theorem and the Empirical Rule? Check all that apply.
Chebyshev's theorem applies to any set of values. Chebyshev's theorem works for symmetrical, bell-shaped distributions.
Which of the following would be calculated using the geometric mean? Select all that apply.
Average percentage annual yield for a portfolio of stocks. Average growth rate for four years of sales figures.
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 data is bimodal. The most frequent observation is much higher or much lower than most of the data values. No observation occurs more than once.
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
The mode can be computed for which of the following levels of data?
Nominal, Ordinal, Interval, and Ratio
Sample standard deviation is:
the square root of sample variance
