Buisness Stats 1 Ch.3 DSM

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 lets us compare the number of observations in two or more sets of data.

Which of the following is true regarding medians and means?

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

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

Nominal Ordinal

Sample standard deviation is:

the square root of sample variance

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.

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.

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

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

The number of observations in the population

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

A measure of location

Which one of the following is true for a positively skewed distribution?

A small number of observations are much larger in value than most of the 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).

Which one of the following is true for a symmetrical distribution?

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

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

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

7

The average age of undergraduate students at Grand Canyon University is 44. If the standard deviation is 4, what percentage of undergraduate students are between 36 and 52 years old?

75% Not: 89% This would be true if k=3, but k=2 because (36-44)/4 = -2 and (52-44)/4 = 2

Which one of the following is an unethical approach to reporting statistics?

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

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.

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.

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

True or false: The standard deviation is a measure of dispersion.

TRUE

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

The sample size

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 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. Reason: A measure of location is often referred to as an average.

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.

A statistic is:

a characteristic of a sample

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.

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

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

range

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

--Chebyshev's theorem applies to any set of values. --Chebyshev's theorem works for symmetrical, bell-shaped distributions. ---The Empiricial Rule works for any distribution.

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

--Interval level data --Ratio level data --Ordinal level data

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 the correct formula for the population variance?

......

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

12.50

What is the variance of the following sample data? 2, 6, 2, 10

14.67

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

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% Reason: The waiting time of the patients in the emergency room between 1 hour and 2 hours is correct if it lies within plus and minus three standard deviations of the mean. x⎯⎯−3s=90−(3*10)=60 = 1 hourx⎯⎯+3s=90+(3*10)=120=2 hoursx¯-3s=90-(3*10)=60 = 1 hourx¯+3s=90+(3*10)=120=2 hours Therefore, approximately 99.7% of the emergency room patients will wait between 1 hour and 2 hours.

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 accurately describes the median of a set of data?

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

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.

The Population Mean is:

the arithmetic mean of all of the values in the population

he formula for the weighted mean is Xw=Σ(wX)/Σw 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 a special case of the arithmetic mean. --It is not unduly influenced by very large or very small values --It is used when there are several observations of the same value.

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

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

What is the standard deviation of the following population data? 3, 1, 2, 9, 5

2.83

What is the variance of the following population data? 2, 6, 1

4.67

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

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

What is the standard deviation of the following sample data? 7, 6, 2, 0, 5

2.92

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

8.00

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

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.

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.

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

FALSE

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, ...)

Which one of the following is a statistic?

the mean of a sample

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

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

the number of values in the sample.