ch 3

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.

What does a measure of dispersion tell us about a set of data?

It tells us about the spread of the data.

When you calculate the sample mean, you divide the sum of the values in the sample by

the number of values in the sample.

Given the following population data sets, which has a smaller population variance?

12, 14, 15, 12, 14, 13

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

A measure of location

For which of the following variables can one calculate a median?

Daily temperatures in August for the past 10 years Shoe size Finishing position in a marathon (1st, 2nd, 3rd, ...)

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 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 level data Ratio level data Ordinal level data

Which of the following statements are reasons to study the dispersion of data? Select all that apply.

It allows us to compare the spread in two or more distributions. A small value for dispersion indicates that the data is closely clustered around the center

Of the following, which one is an advantage of the standard deviation over the variance?

It is in the same units as the data.

Given the following population data sets, which has a smaller population variance?

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 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 is an advantage of the range compared to the variance? Check all that apply.

It is simpler to understand and calculate.

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.

It is used when there are several observations of the same value. 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 with data that has repeated values, such as a frequency distribution.

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

Nominal Ordinal

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.

Suppose a population is made up of the following values: 1, 8, 5, 6. What is the population mean?

Reason: (1 + 8 + 5 + 6)/4 = 20/4 = 5

Which of the following is true regarding medians and means?

Reason: Both can be calculated from ratio-level data. Reason: Neither can be calculated from nominal-level data. Reason: Both can be calculated from interval-level data.

Which measure of dispersion results in units that are different from the data?

Variance

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. Reason: Extreme values impact the mean much more than the median.

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 For skewed distributions, the median will always be between the mode and mean and the mean will be the value furtherest in the direction of the skew.

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

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

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} Reason: The value {1} is much smaller than the rest of the data.

Which of the following are important properties of the arithmetic mean? Check all that apply.

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. There is only one mean for a set of data.

The larger the population variance is for a data set,

the more spread out the data is

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 two 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.

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).

the more spread out the data is Population variance measures the spread of the data, not the center

The larger the population variance is for a data set,

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 statements best defines the mode?

The value of the observation that appears most frequently.

What is the purpose of a measure of location?

To indicate the center of a distribution of data.

Which one of the following is a statistic?

the mean of a sample

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.