Chapter 3: Describing Data: Numerical Measures
Which of the following accurately describes the median of a set of data?
The midpoint of the data when it is arranged in order.
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
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.
Choose the formula for the Sample Variance.
Σ(X−X)2n−1
Which of the following is the correct formula for the population variance?
Σ(X−μ)2N
Suppose a population is made up of the following values: 1, 8, 5, 6. What is the population mean?
5
What is the range for the following set of data? 3, 5, 4, 6, 7, 10, 9
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%
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.
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 variance is a measure of central tendency.
False
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.
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 measure of dispersion results in units that are different from the data?
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
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.
The formula for the weighted mean is X𝑋w=Σ(wX)ΣwΣ(wX)Σ𝑤 Which of the following statements are true of the weighted mean?
It is a special case of the arithmetic mean. The denominator of the weighted mean is always the sum of the weights. It is used when there are several observations of the same value.
What does a measure of dispersion tell us about a set of data?
It tells us about the spread of the data.
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.
The mean, median, and mode are all the same for which type of distribution?
Symmetrical distribution
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.
Which of the following are important properties of the arithmetic mean?
There is only one mean for a set of data. All of the values in the data are used in calculating the mean. Σ(X-X𝑋)=0 i.e. the sum of the deviations is zero.
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.
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
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.
68%
plus or minus one standard deviation.
99.7%
plus or minus three standard deviations
95%
plus or minus two standard deviations
The difference between the largest and the smallest values in a data set is called the ______.
range
What is another term for the "average" value of a distribution?
A measure of location
Choose the best definition for the variance.
The arithmetic average of the squared deviations from the mean.
