Business Statistics Chapter 3
The mode can be computed for which of the following levels of data?
nominal, ordinal, interval, ratio
When you calculate the sample mean, you divide the sum of the values in the sample by
number of values in a sample
For a data set with an odd number of observations that have been sorted from smallest to largest values. Where is the median located?
observation in the middle
The difference between the largest and the smallest values in the data set is called the ____.
range
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
The Population Mean is:
the arithmetic mean of all the values in a population
The larger the population variance is for a data set
the more spread out the data is
The larger the population variance is for a data set,
the more spread out the data is
Sample standard deviation is
the square root of the sample variance
Which of the following statements best defines the mode?
the value of the observation that appears most frequently
The net incomes (in $millions) of a sample of steel fabricators are $86, $67, $86, and $85. What is the modal net income?
$86
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.
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 negatively skewed distribution?
There are a small number of observations that are much lower in value than most of the data.
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
What characteristic of a data set that 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 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 main much more than the median.
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 is an advantage of the range compared to the variance?
It is simpler to understand and calculate
Which of the following statements are true of the weighted 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. It is a special case of the arithmetic mean.
What does a measure of dispersion tell us about a set of data?
It tells us about the spread of the 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
Chebyshev's Theorem states that the proportion of values is at least 1-1/k^2. Where:
Kate is the number of standard deviations, greater than one, within which that proportion of observations will be found
The mean, as a measure of central location, would be inappropriate for which one of the following?
Marital status of college students at a particular university
For the past week accompanies common stock closed with the following prices: $61.50, $62, $61.25, $60.875, and $61.5. What is the price range?
$1.125
Which of the following are important properties of the arithmetic mean?
- all of the values in the data are used in calculating the mean - there is only one mean for a set of data - the sum of the deviations is zero
Given the following population data set, which has a smaller population variance?
12,14,15,12,14,13
What is the variance of the following sample data? 2, 6, 2, 10
14.67
A sample of small bottles and their contents has the following weights in grams: 4, 2, 5, 4, 5, 2 and 6. What is the sample variance of bottle weight?
2.33. The sample mean is (4+2+5+4+5+2+6)/7= 4. Then use formula 3-9: s^2 = (4-4)^2+(2-4)^2+(5-4)^2+(4-4)^2+(5-4)^2+(2-4)^2+(6-4)^2/7-1 = 14/6 = 2.33
A sample of single persons receiving Social Security payments revealed these monthly benefits: $826, $699, $1,087, $880, $839, and $965. How many observations are below the median?
3
The investment research Institute reported and its mutual fund fact book that the number of mutual funds increased from 5725 to 7977 over a 10-year period. What is the geometric mean annual percent increase in the number of funds??
3.37%. GM= n square room of value at end of period/value at start of period -1 = 10 square root 7,977/5,725 - 1= 1.0337 - 1 = 0.0337 or 3.37%
Suppose a population is made up of the following values: one, eight, five, six. What is the population mean?
5. (1+8+5+6)/4=5
The empirical role states that approximately what percentage of observations we 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. 95% - plus or minus 2 standard deviations. 99.7% - plus or minus 3 standard deviations
What is the variance of the following sample data? 8, 6, 2, 8
8
What is the range for the following set of data? 4, 12, 5, 3, 7, 8, 9
9
Suppose the wait time at the emergency room follow a symmetrical bell shaped distribution with a mean of 90 minutes in standard deviation of 10 minutes. What percentage of emergency room patients will wait between one hour and two hours?
99.7%
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.
The main, median, and mode are all the same for which type of distribution?
A symmetrical distribution
A population consists of all the weights of all defensive tackles on universities football team. They are Johnson 204 pounds; Patrick 215 pounds; Junior 207 pounds; kendron 212 pounds; nicko 214 pounds; Cochran 208 pounds. What is the population standard deviation in pounds?
About 4
The weighted mean provides a way to compute the ____ mean when there are several observations of the same value.
Arithmetic
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
True or false: the variance is a measure of central tendency
False
For which of the following variables can one calculate a median?
Finishing position in a marathon (1st, 2nd, 3rd, ...) - ordinal data Daily temperatures in August for the past 10 years Shoe size - interval data
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.
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.
A question in a market survey asks for a respondents favorite car color. Which measure of central location should we use to summarize this question?
Mode
Most of the used cars sold by a used car dealer a 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
Which one of the following is true regarding the use of mode, mean, and median for different levels of measurement?
Only the mode can be used for nominal-level data.
Which of the following kinds of data can be used to find a medium value?
Ordinal level data, interval, level data, ratio level data
In a particular country, most of the households have an annual income of about $20,500. 5% of the households have incomes above $500,000 distribution of income is:
Positively skewed
Choose the best definition for the variance
The arithmetic average of the squared deviations from the mean.
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.
A purchasing agent for a trucking company is shopping for replacement tires for the trucks from two suppliers. The suppliers prices are the same however supplier tires have an average life of 60,000 miles with a standard deviation of 10,000 miles supplier tires have an average life of 60,000 miles with a standard deviation of 2000 miles.
The life of supplier bees tires is more predictable than the life of supplier A's tires
Which of the following accurately describes the median of a set of data?
The midpoint of the data when it is arranged in order.
The median is defined as:
The midpoint of the values after they have been arranged in rank order
What does end 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 sample variances?
The sample variance measures deviations from the sample meme, whereas the population variance uses the population mean
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 another term for the "average" value of a distribution?
measure of location
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
Which measure of dispersion results in units that are different from the data?
variance
The median would be a better measure for the center for which of the following data sets?
{9,11,14,16,1,12,15,17}
formula for sample variance
Σ ( X- x with Line over)² / n-1
population variance formula
σ² = Σ ( X- μ )² / N
