Chapter 3 SmartBook

Σ(x−μ)2/N

Which of the following is the correct formula for the population variance? ΣX−μn−1Σ�-μ�-1 Σ||X−μ||nΣ|�-μ|� Σ(x−μ)2N

Sum the values in the population and then divide by the number of values in the population.

How do you find the Population Mean for a set of data? Take the number of objects in the population and divide by the sum of all the values. Sum the values in the population and then divide by the number of values in the population. Arrange the values in rank order and select the one in the middle.

False

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

It is in the same units as the data.

Of the following, which one is an advantage of the standard deviation over the variance? It can be used to compare different sets of data. It is easier to calculate. It is in the same units as the data. It uses all of the values in the set of data.

It is in the same units as the data.

Of the following, which one is an advantage of the standard deviation over the variance? It is in the same units as the data. It can be used to compare different sets of data. It uses all of the values in the set of data. It is easier to calculate.

Daily temperatures in August for the past 10 years Time to run a marathon

Select all that apply For which of the following variables can one calculate an arithmetic mean? Daily temperatures in August for the past 10 years Colors of cars Time to run a marathon Finishing position in a marathon (1st, 2nd, 3rd, ...)

The variance would be in ounces-squared.

Given the following weights (in ounces) of four apples, 6, 8, 10, and 7, which of the following is true? The mean, median, and mode would be in ounces-squared. The variance would be in ounces-squared. The range would be in ounces-squared. The standard deviation would be in ounces-squared.

Sum the values in the population and then divide by the number of values in the population.

How do you find the Population Mean for a set of data? Take the number of objects in the population and divide by the sum of all the values. Arrange the values in rank order and select the one in the middle. Sum the values in the population and then divide by the number of values in the population.

the midpoint of a given class

In the formula for calculating the mean of grouped data, M stands for: the minimum value in a given class the maximum value in a given class the midpoint of a given class

symmetrically distributed

In the library of a small town, the mean cost of new books is the same as the median cost of new books. The distribution of book costs is: symmetrically distributed negatively skewed positively skewed

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.

Select all that apply 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. It lets us compare the number of observations in two or more sets of data. It allows us to compare the central values of two or more distributions.

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

Select all that apply Which of the following would be calculated using the geometric mean? Select all that apply. Average rainfall for a series of ten years. Average percentage annual yield for a portfolio of stocks. Average growth rate for four years of sales figures. Average number of items sold on six consecutive days at a store.

5

Suppose a population is made up of the following values: 1, 8, 5, 6. What is the population mean? 1 8 4 7 5

99.7%

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% 88.9% 95% 68%

7

What is the range for the following set of data? 3, 5, 4, 6, 7, 10, 9 3 10 7 6

9

What is the range for the following set of data? 4, 12, 5, 3, 7, 8, 9 12 3 7 9

k is the number of standard deviations, greater than 1, within which that proportion of observations will be found.

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. k is the number, greater than one, found by counting the standard deviations between the sample and population. k is the number of observations required for a sample that will give a good population estimate.

The number of observations in the population

What does N represent in the formula for the population variance? The sample size The number of observations in the population The arithmetic mean of the population

It tells us about the spread of the data.

What does a measure of dispersion tell us about a set of data? It tells us about the spread of the data. It tells us how fast the values change within the set of data. It describes the central tendency of the data. It tells us the distance between adjacent values in the data.

The number of observations in the sample

What does n represent in the formula for the sample variance? The number of observations in the population The sample variance The number of observations in the sample

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

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). For sample mean, the sum of values is divided by the number of values minus one. To calculate the sample mean, you divide by the sample number plus one.

All of the values in the data are used in calculating the mean. There is only one mean for a set of data. Σ(X-X�)=0 i.e. the sum of the deviations is zero.

Select all that apply Which of the following are important properties of the arithmetic mean? Check all that apply. All of the values in the data are used in calculating the mean. The mean can be calculated for nominal data. The mean is always less than the median. There is only one mean for a set of data. Σ(X-X�)=0 i.e. the sum of the deviations is zero.

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.

Select all that apply 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 miles per hour of 6 cars measured at an intersection, The average annual rate of return for a mutual fund held for five years. The average income for the households in a neighborhood.

the arithmetic mean of all of the values in the population

The Population Mean is: is pronounced "moo" (like the sound a cow makes) the median value of the observations in the population the arithmetic mean of all of the values in the population the most common value in the population

It indicates that the data is closely clustered around the center.

What does a small value for a measure of dispersion tell us about a set of data? It shows that the values of the data are widely separated. It indicates that the data is closely clustered around the center. It indicates that there are not very many values within the set of data.

The sample standard deviation

What does s represent in the formula for the standard deviation of grouped data variance? The class frequency The sample size The sample standard deviation

A measure of location

What is another term for the "average" value of a distribution? A measure of location The distribution peak The measure of dispersion The normal value

To indicate the center of a distribution of data.

What is the purpose of a measure of location? To indicate the upper and lower values in a data set. To indicate the center of a distribution of data. To measure the shape of a distribution. To show where a specific value is located in a set of data.

the number of values in the sample.

When you calculate the sample mean, you divide the sum of the values in the sample by the sample number minus one. the number of non-repeating sample values. the number of values in the sample.

s=√f(M−x)2n−1

Which of the following is the correct formula for the standard deviation of grouped data?

Each of the measures has advantages and disadvantages in representing the data.

Why is it important to consider all the measures of location in reporting statistics? Each of the measures has advantages and disadvantages in representing the data. The mean is the best representation for skewed data. For a symmetrical distribution they all have the same value.

The value of the observation that appears most frequently.

Which of the following statements best defines the mode? Any value that appears in the data more than once. The arithmetic average of the data. The value that is the midpoint of the data. The value of the observation that appears most frequently.

It is only an estimate of the corresponding actual value.

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. It is more precise to calculate the values from grouped data than to use the raw data. It is easier to calculate than using the actual values.

The mean, median and mode all have the same value.

Which one of the following is true for a symmetrical distribution? The mode is the best choice of measure of location. The mean is greater that the median. The mean, median and mode all have the same value. The mean is less than the median.

Only the frequency distribution data is available.

Why would one use a grouped mean or standard deviation? A grouped mean or standard deviation calculation is more accurate. Only the frequency distribution data is available. Software packages make it easy to calculate the grouped mean and grouped standard deviation

1-1/k2 for k>1

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 11−k211-�2 for k>1 1−k2k1-�2� for k>1

Σ(X−X)2/n−1

Choose the formula for the Sample Variance. Σ(X−X)2n−1Σ(�-�)2�-1 Σ(x−μ)2NΣ(�-μ)2� Σ|||X−X|||n−1

range

The difference between the largest and the smallest values in a data set is called the Blank______. mean median range mode

X�=ΣfMn

Which of the following is the correct formula for the Mean of Grouped Data? X�=ΣXnΣ�� X�=ΣfMnΣfM� X�=Σ(X−X)2n−1

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.

The formula for the weighted mean is X�w=Σ(wX)ΣwΣ(wX)Σ� Which of the following statements are true of the weighted mean? Select all that apply. It gives a larger value for the mean than the formula for the arithmetic mean. 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.

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

Which of the following accurately describes the median of a set of data? The difference in the largest and smallest values. The arithmetic average of the values in the set. The midpoint of the data when it is arranged in order. The most numerous observation in a set of data.

The arithmetic average of the squared deviations from the mean

Which of the following defines variance? The difference between the largest and the smallest value from the set of data The arithmetic average of the absolute value of the deviations from the mean The arithmetic average of the squared deviations from the mean

Measures of location do not tell us about the spread or clustering of data.

Why is it important to consider measures of dispersion as well as measures of location when reporting statistics? The mode is the best measure of location. Measures of location do not tell us about the spread or clustering of data. in skewed distributions the mean and median are not equal.

68% plus or minus one standard deviation. 95% plus or minus two standard deviations 99.7% plus or minus three standard deviations

The Empirical rule states approximately what percentage of observations will be found within some deviation from the mean for a normal distribution. Match the percentage of observation to the range. 68% 95% 99.7% plus or minus one standard deviation. plus or minus two standard deviations plus or minus three standard deviations

Giving only the measures of location and dispersion that support your point of view.

Which one of the following is an unethical approach to reporting statistics? Reporting all three measures of location. Always reporting a representative measure of dispersion in addition to a measure of location. Giving only the measures of location and dispersion that support your point of view.

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. It is a special case of the arithmetic mean.

Select all that apply The formula for the weighted mean is X�w=Σ(wX)ΣwΣ(wX)Σ� 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. The denominator of the weighted mean is always the sum of the weights. It is a special case of the arithmetic mean. It gives a larger value for the mean than the formula for the arithmetic mean.

For many sets of data there is no mode. For many sets of data there are multiple modes.

Select all that apply 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. The mode is affected by extremely large and small values. the mode can only be computed for interval-level data or higher

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 formula for the weighted mean is X�w=Σ(wX)ΣwΣ(wX)Σ� Which of the following statements are true of the weighted mean? Select all that apply. It is not unduly influenced by very large or very small values The denominator of the weighted mean is always the sum of the weights. It gives a smaller value for the mean than the formula for the arithmetic mean. It is used with data that has repeated values, such as a frequency distribution.