Chapter 3

Which of the following statements best defines the mode?

The value of the observation that appears most frequently.

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 accurately describes the median of a set of data?

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

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

Ordinal level data Ratio level data Interval level data

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 sample data? 2, 6, 2, 10

14.67

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

5 because (1 + 8 + 5 + 6)/4 = 20/4 = 5

True or false: The variance is a measure of central tendency.

False

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.

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

It is in the same units as the data.

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

It tells us about the spread of the data.

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.

Choose 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 population mean?

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

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.

What is the variance of the following sample data? 8, 6, 2, 8

8

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

A measure of location

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

A symmetrical distribution.

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.

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

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

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 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 difference between the largest and the smallest values in a data set is called the ______.

range

The Population Mean is:

the arithmetic mean of all of the values in the population

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 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.

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

What does N represent in the formula for the population variance?

the number of observations in the population

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

the number of values in the sample.

Sample standard deviation is:

the square root of sample variance

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.