Statistics LearnSmart Ch. 3

True or false? 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 kinds of data can be used to find a median value?

Interval, ordinal, ratio

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.

What 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 is an advantage of the range compared to the variance?

It is simpler to understand and calculate

Chebyshev's Theorem states that the proportion of values is at least 1-1/k^2. 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.

Most of the items sold at a garage sale cost about $12. Nothing sold for more than $15, but some items only cost a few cents. What would be the best measure of the center of the distribution of sale prices?

Median

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 have income above 1,000,000?

Median

The mean, median, and mode are all the same for which type of distribution?

Symmetrical distribution

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 is the best definition for the variance?

The arithmetic average of the squared deviations from the mean

How does the formula for the sample mean differ from the formula for the population mean?

The formulas are functionally the same, but 'n' (sample size) is used instead of 'N' (population size).

Which of the following accurately describe the median of a set of data?

The midpoint of the data when it is arranged in order.

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

Which of the following are important properties of the arithmetic mean?

-All of the values in the data are used in calculating the mean -The sum of the deviations is zero -There is only one mean for a set of data

Which of the following would be calculated using the geometric mean?

-Average growth rate for four years of sales figures -Average percentage annual yield for a portfolio of stocks

Which of the following is true regarding the application of Chebyshev's theorem and the Empirical Rule? Select all that apply.

-Chebyshev's theorem applies to any set of values -Chebyshev's theorem works for symmetrical, bell-shaped distributions

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

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 of the following statements describe weaknesses of the range as a measure of dispersion?

-It may be unduly influenced by an unusually large value -It may be unduly influenced by an especially small value -Only two values from the data set are used

Which of the following are advantages of the variance compared to the range?

-It uses all values in the data, not just two -It is not unduly influenced by large or small values

Which of the following is true regarding the application of Chebyshev's theorem and the Empirical Rule?

-The Empirical Rule gives more precise answers for the symmetrical, bell-shaped distribution -Only Chebyshev's applies to skewed distributions

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 are reasons why the mode would not be a good choice of measure for describing the center of a set of data?

-The data is bimodal -The most frequent observation is much higher or lower than most of the data values -No observation occurs more than once

Which of the following statements are true of the weighted 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 -It is a special case of the arithmetic mean

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

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/k^2 for k>1

What is the variance of the following population data? 2, 0, 1, 9

12.5

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 set? 7, 6, 2, 0, 5

2.92

A mutual fund has a rate of return for five years of 10%, 14%, -20%, 18%, and 22%. Calculate the geometric mean (average rate of return)

7.6%

According to Chebyshev's theorem, what proportion of observations will lie within 3 standard deviations of the mean for a positively skewed distribution?

8/9, 89%

A statistic is?

A characteristic of a sample

What is another term for the "average" value of a distribution?

A measure of location

Which of the following is true regarding medians and means?

Medians can be calculated from ordinal-level data, but means can't

For a positively skewed distribution, the ordering of the median, mode, and mean, from least to greatest, would be what?

Mode, median, mean

The mode can be computed for which of the following levels of data?

Nominal, ordinal, interval, and ratio

Which 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

What does 'n' represent in the formula for the sample variance?

The number of observations in the population

Which statement is true with regard to differences in the formula for the population and sample variances?

The sample variance measures deviations from the sample mean, whereas the population variance uses the population mean.

What is the sample standard deviation?

The square root of sample variance

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

What is the purpose of a measure of location?

To indicate the center of a distribution of data

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

Which of the following are used to measure dispersion?

Variance, range, and SD

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.