MBA 513 mod 1 ch3
The larger the population variance is for a data set,
the more spread out the data is
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.
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.
Most of the items sold at a garage sale cost about $12. Nothing sold for more than $15, but a few items cost only 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 of households have incomes above $1,000,000?
Median
In 2004 a new car cost $32,000. In 2016 a comparable model cost $54,000. Which of the following will best represent the average annual increase in cost of the car?
The Rate of Increase over time formula
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.
Choose the best definition for the variance.
The arithmetic average of the squared deviations from the mean.
Which of the following statements best describes the strength of the range as a measure of dispersion?
The calculation is easy to perform.
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.
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.
Which statement best describes the difference between the formula for Population and Sample variance?
Which statement best describes the difference between the formula for Population and Sample variance?
A statistic is:
a characteristic of a sample
The Population Mean is:
the arithmetic mean of all of the values in the population
The median is defined as:
the midpoint of the values after they have been arranged in rank order
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
The dispersion of a set of data is often referred to as:
variation or spread
The median would be a better measure for the center for which of the following data sets? {0.9, 1.2, 2.2, 1.6, 2.1, 3} {9, 11, 14, 16, 1, 12, 15, 17} {6, 6, 6, 7, 7, 8, 8, 8, 8, 9} {4, 6, 5, 8, 3, 4, 7, 5}
{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?
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.
Which of the following are advantages of the variance compared to the range?
-It uses all of the values in the data, not just two. -It is not unduly influenced by large or small values.
Which of the following are reasons why the mode would not be a good choice of measure for the describing the center of a set of data?
-No observation occurs more than once. -The data is bimodal. -The most frequent observation is much higher or much lower than most of the data values.
Which of the following statements are reasons to study the dispersion of data?
-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.
Which of the following would be calculated using the geometric mean? Select all that apply.
-Average growth rate for four years of sales figures. -Average percentage annual yield for a portfolio of stocks.
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 of the following are disadvantages of the mode?
-For many sets of data there are multiple modes. -For many sets of data there is no mode.
Which of the following kinds of data can be used to find a median value?
-Interval level data -Ordinal level data -Ratio level data
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.
mean plus or minus three standard deviations
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% Reason: (camera roll)
What is the definition of "parameter"?
A characteristic of a population.
What is another term for the "average" value of a distribution?
A measure of location
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 Reason: The variance is a measure of dispersion
Which of the following is true regarding the application of Chebyshev's theorem and the Empirical Rule?
-Only Chebyshev's applies to skewed distributions. -The Empirical Rule gives more precise answers for the symmetrical, bell-shaped distribution. -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?
-Shoe size -Daily temperatures in August for the past 10 years -Finishing position in a marathon (1st, 2nd, 3rd, ...)
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 statements represent an ethical approach to the use of statistics?
-We must maintain an independent and principled point of view. -A statistical report requires objective and honest communication of results.
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
Given the following population data sets, which has a smaller population variance? 10, 18, 20, 25 12, 14, 15, 12, 14, 13 10, 16, 18, 12, 14 10, 15, 20
12, 14, 15, 12, 14, 13 reason: 10, 18, 20, 25 (This data set has the most variation.) 10, 16, 18, 12, 14 (This data is not the least spread out.) 10, 15, 20 (This data set has the fewest observations, but its data is not the least spread out.)
What is the variance of the following population data? 2, 0, 1, 9
12.50 reason: ?
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% reason: (camera roll)
What is the variance of the following sample data? 2, 6, 2, 10
14.67 use excel =var.s
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
Which of the following is the correct formula for the population variance?
2.83 how?
What is the standard deviation of the following sample data? 7, 6, 2, 0, 5
2.92
A house that sold for $340,000 in 2009 sold for $420,000 in 2016. What was the annual rate of increase of the price?
3.1% reason: use geometric mean (on camera roll)
What is the variance of the following population data? 2, 6, 1
4.67 how?
Find the median for the following sample of data: 8, 4, 5, 13, 1, 8, 3.
5
Find the median for the following sample of data: 8, 1, 6, 6, 4, 8, 2, 8, 20.
6 reason: 20, 8, 8, 8, (6,) 6, 4, 2, 1
Find the median for the following sample of data: 8, 3, 6, 6, 4, 8, 8, 7.
6.5 reason: 8 8 8 7 6 6 4 3
mean plus or minus one standard deviation.
68%
Calculate the mean of the following sample of data: 12, 4, 5.
7
What is the range for the following set of data? 3, 5, 4, 6, 7, 10, 9
7 reason: 10 - 3 = 7
Calculate the mean of the following sample of data: 12, 4, 6, 6.
7 reason: 12 + 4 + 6 + 6 = 28 28 / 4 = 7
A mutual fund has a rate of return for five years of 10%, 14%, -20%, 18%, and 22%. Calculate the average rate of return (geometric mean). Round to the nearest tenth of a percent.
7.6% reason: (camera roll)
According to Chebyshev's theorem, what proportion of values for a bimodal distribution will be found within two standard deviations of the mean?
75% reason: 1-1/2^2= 3/4
What is the variance of the following sample data? 8, 6, 2, 8
8.00 use excel =var.s
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 reason: 1-1/3^2= 8/9
What is the range for the following set of data? 4, 12, 5, 3, 7, 8, 9
9 reason: it is the maximum minus the minimum 12 - 3 = 9
mean plus or minus two standard deviations
95%
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.
The mean, median, and mode are all the same for which type of distribution?
A symmetrical distribution.
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, Interval, and Ratio
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 are used to measure dispersion? SRV
Standard Deviation Range Variance
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.
What does N represent in the formula for the population variance?
The number of observations in the population
What does n represent in the formula for the sample variance?
The number of observations in the sample
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.
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 Reason: the units are the square of the data's units.
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
the weighted mean provides a way to compute the ________ mean when there are several observations of the same value.
arithmetic
True or false: It is appropriate to remove outliers in the data set to make the data easier to analyze.
false Reason: Integrity of raw data must be maintained.
Chebyshev's Theorem states that the proportion of values is at least 1-1/k2. Where:
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 mean of a sample is a:
statistic
