Chapter 3
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
A stock has returns for four years of 5%, 17%, 64%, and -35%. Calculate the average annual rate of return (geometric mean).
6.98%
Which of the following are important properties of the arithmetic mean?
- all of the values in the data are used in calculating the mean - there is only one mean for a set of data - the sum of the deviations is zero
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 - the empirical rule gives more precise answers for symmetrical, bell-shaped distribution - only chebyshev's applies to skewed distributions
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 are disadvantages of the mode?
- for many sets of data there are multiple modes - for many sets of data there is no mode
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
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
Which of the following kinds of data can be used to find a median value?
- ratio level data - ordinal level data - interval level data
Which of the following averages would be calculated using the geometric mean?
- the average annual rate of return for a mutual fund held for 5 years - the average annual rate of growth of undergraduate enrollment for the last 10 years - average growth rate for four years of sales figures - average percentage annual yield for a portfolio of stocks
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?
- the data is bimodal - no observation occurs more than once - the most frequent observation is much higher or much lower than most of the data values
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 frequency distribution - it is a special case of the arithmetic mean
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
12.5
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
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%
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).
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%
What is the variance of the following sample data? 8, 6, 2, 8
8
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
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
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
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
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
The mode can be computed for which of the following levels of data?
nominal, ordinal, interval, and ratio
Which one of the following is true regarding the use of the mode, mean, and median for different levels of measurement?
only mode can be used for nominal-level data
Why would one use a grouped mean or standard deviation?
only the frequency distribution data is available
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
Which of the following are used to measure dispersion?
standard deviation, range, and variance
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
The population mean is:
the arithmetic mean of all of the values in the population
Which of the following statements best describes the strength of the range as a measure of dispersion?
the calculation is easy to perform
Which one of the following is a statistic?
the mean of a sample
In the formula for calculating the mean of grouped data, M stands for:
the midpoint of a given class
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
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? Multiple choice question.
the sample standard deviation
Sample standard deviation is:
the square root of sample variance
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 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
What is the purpose of a measure of location?
to indicate the center of a distribution of data
Which measure of dispersion results in units that are different from the data?
variance
The dispersion of a set of data is often referred to as which of the following?
variation or spread
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
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
T/F: The variance is a measure of central tendency.
False
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 true regarding medians and means?
medians can be calculated from ordinal-level data, but means can't
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.
What is the definition of "parameter"?
a characteristic of a POPULATION
A statistic is:
a characteristic of a sample
What is another term for the "average" value of a distribution?
a measure of location
Which one of the following is true for a positively skewed distribution?
a small number of observations are much larger in value than most of the data
The mean, median, and mode are all the same for which type of distribution?
a symmetrical distribution