BUS Stat. Ch. 3
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
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.
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 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 are important properties of the arithmetic mean? Check all that apply.
There is only one mean for a set of data. Σ(X-XX)=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 measure of dispersion results in units that are different from the data?
Variance
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.
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 unusually large value It may be unduly influenced by an especially small value.
The Population Mean is:
the arithmetic mean of all of the values in the population
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
True or false: It is appropriate to remove outliers in the data set to make the data easier to analyze.
False
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.
What does n represent in the formula for the sample variance?
The sample size
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 apply.
It is a special case of the arithmetic mean. It is used when there are several observations of the same value. The denominator of the weighted mean is always the sum of the weights.
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
For which of the following variables can one calculate an arithmetic mean?
Time to run a marathon Daily temperatures in August for the past 10 years
True or false: The standard deviation is a measure of dispersion.
True
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 standard deviation of the following sample data? 2, 6, 2, 0, 5
2.45
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
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.
Which of the following statements represent an ethical approach to the use of statistics? Check all that apply.
A statistical report requires objective and honest communication of results. We must maintain an independent and principled point of view.
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 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.
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
The mode can be computed for which of the following levels of data?
Ordinal Nominal
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 is true regarding the application of Chebyshev's theorem and the Empirical Rule? Check all that apply.
The Empirical Rule gives more precise answers for the symmetrical, bell-shaped distribution. Only Chebyshev's applies to skewed distributions.
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.
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 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.
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.
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.
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
In a particular country most of the households have an annual income of about $20,500. Five percent of the households have incomes above $500,000. The distribution of income is:
positively skewed
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 range for the following set of data? 3, 5, 4, 6, 7, 10, 9
7
What is the variance of the following population data? 2, 0, 1, 9
12.50
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.
