Chapter 3 assign.
Which of the following correlation coefficients indicates the strongest inverse relationship between the two variables?
-0.87
What is the range of possible values for the correlation coefficient?
-1 to 1
When the correlation coefficient approaches the value ______, it indicates that there is a weak relationship between the two variables.
0
The Sharpe ratios for four investments are listed below. Assuming that all other characteristics of these investments are the same, a rational investor would select the investment with a Sharpe ratio of ______.
0.59 Reason: The larger the ratio, the better the compensation for the risk taken.
When a box plot is constructed, an outlier is a data point that is farther than ______.
1.5×IQR from either Q1 or Q3
Suppose that the 12th percentile of starting salaries for accounting graduates from your college is $41,000. What does this mean?
12% of the graduates earn less than $41,000.
If Lp for a given percentile equals 8.3, then the percentile is
30% of the way from the 8th to the 9th smallest values.
Quartiles divide the data into ______ equal parts.
4
Consider the following data set: 4, 4, 5, 6, 9, 9. Find the mode(s).
4 and 9
If the median price for a home is $200,000, then ______ of the homes cost less than $200,000.
50% Reason: The median is the middle value so half of the values will fall below the median and half will fall above the median.
In which of the following data sets would the arithmetic mean NOT be a good measure of central location?
7, 8, 8, 9, 25 Reason: The value "25" is an outlier in this data set. The median is a better choice.
Pat's time in the 1600-meter run placed Pat in the 85th percentile in the school. What percentage of students are faster than Pat?
85%
The empirical rule states that approximately ______ of observations will fall within two standard deviations of the mean.
95%
Which of the following is true when using the empirical rule for a sample of observations?
Approximately 68% of the observations are in the intervall x ± 1s
The owner of BevaMart wants to study the relationship between the outside temperature and hot chocolate sales. The owner found the covariance between the two variables outside to be -81.46. Based on the covariance, which option best describes the linear relationship between temperature and hot chocolate?
As the temperature increases, hot chocolate sales decrease.
Which of the following are true about Chebyshev's theorem and the Empirical Rule? Select all that apply.
Both work for bell-shaped data, but the Empirical Rule is more precise.
What is the first step in the process to calculate the mean absolute deviation?
Calculate the arithmetic mean for the data set. Reason: You need to find the mean first so you can find the difference between each observation and the mean.
True or false: The term central location relates to the way qualitative data tend to cluster around a lower value.
False Reason: The term central location relates to the way QUANTITATIVE data tend to cluster around a TYPICAL OR CENTRAL value.
Which of the following are true? Select all that apply.
Half the data is below the second quartile. The second quartile equals the median.
Which of the following are true about the mean absolute deviation?
It increases as data becomes more spread out. It can never be negative.
Which of the following statements about the mean absolute deviation (MAD) is MOST accurate?
MAD is expressed in the same units as the original data.
What is the most widely-used measure of central location?
Mean
In a neighborhood there are five houses listed for sale for the following amounts: $250,000; $275,000; $280,000; $295,000; and $515,000. What is the BEST measure of central location for the price of a house in the neighborhood?
Median
For a qualitative data set, the most meaningful measure of central location is the ______.
Mode Reason: Calculating the mean would require starting with quantitative (numerical) data.
The symbol x represents the ______.
Sample mean population mean: μ. population variance: σ2. sample variance: s2.
A researcher wants to compare the variability of two data sets that have different units of measurement. Which of the following measures is MOST useful as a relative measure of dispersion?
The coefficient of variation
A researcher wants to compare the variability of two data sets that have different units of measurement. Which of the following measures is MOSTuseful as a relative measure of dispersion?
The coefficient of variation
Which of the following values is NOT part of the 'five-number summary'?
The mean Reason: The median (second quartile), not the mean, is included.
Mean-variance analysis uses risk and reward to evaluate the rate of return of an asset. How are the risk and reward measured?
The measure associated with risk is the variance, while the measure associated with reward is the mean.
Which of the following values are included in a box plot? Select all that apply.
The median The first quartile The 75th percentile
What is the relationship between the variance and the standard deviation?
The standard deviation is the positive square root of the variance.
Which of the following are true? Select all that apply.
The variance and standard deviation calculate squared deviations. The variance and standard deviation increase as the data becomes more spread out.
Which of the following are true? Select all that apply.
The variance and standard deviation increase as the data becomes more spread out. The variance and standard deviation calculate squared deviations.
Consider the following data set: 4, 5, 6, 9. Find the mode(s).
There is no mode.
True or false: The mean is the most widely used measure of central location for quantitative data.
True
Which of the following statements about variance is MOST accurate?
Variance is the average of the squared deviations from the mean.
Is it possible for a data set to have NO mode?
Yes, if there are no observations that occur more than once.
The coefficient of variation is BEST described as
a relative measure of dispersion.
In order to calculate the arithmetic mean, one
adds all of the data points, then divides by the number of data points.
The correlation coefficient
describes both the direction and the strength of the linear relationship between two random variables.
It is preferable to use the empirical rule if the histogram or other visual and numerical measures suggest a symmetric and bell-shaped distribution.
empirical rule
The interquartile range of a data set
epresents the middle 50% of the data. Reason: The interquartile range represents the middle 50%, after the data are arranged from low to high.
If Fund A has a coefficient of variation of 1.1, and Fund B has a coefficient of variation of 0.9, Fund ______ has the greater relative dispersion.
fund A
Chebyshev's theorem provides the proportion of observations that lie within k standard deviations of the mean. The value k must be ______.
greater than 1
A z-score measures
how many standard deviations a value is from the mean.
The average of the absolute differences between the values of the data set and the mean is the
mean absolute deviation. The arithmetic mean is the additive average of the values in the data set. The standard deviation is calculated by using squared differences from the mean, not absolute differences. The range is the difference between the highest and lowest values in a data set.
The measure of central location where half the values of the data set lie above this measure and half the values of the data set lie below this measure is known as the ______.
median
In general, the best measure of central location for a data set that contains outliers is the ______.
median Reason: The median is calculated as the middle value and so tends not to be influenced by outliers.
An owner of a grocery store wants to determine the brands of soda that customers purchase at the store. When summarizing the data about soda brand purchases, the meaningful measure of central location is the ______.
mode because qualitative
In a box plot, if the median is right of center and the left whisker is longer than the right whisker, then the distribution is
negatively skewed.
The first step to determine the median is to
place the data in numerical order.
The average of the sum of squared differences from the mean is the
population variance.
If the covariance between two random variables x and y is positive, then x and y have a(n) _____.
positive linear relationship
The ______ measures the difference between the largest and smallest values in a data set.
range
The Sharpe ratio determines the additional ______ an investor will receive for each additional unit of risk taken.
reward
Mean-variance analysis is used to measure the performance of an asset based on its rate of return. Specifically, this means evaluating the rate of return on the basis of
risk and reward.
The third quartile is the
same as the 75th percentile.
The notation s2 represents the
sample variance
When calculating a percentile, the first step is to arrange the data set in
sort the data from smallest to largest.
The square root of the average of the sum of squared deviations from the mean is known as the
standard deviation. Mean absolute deviation measures the average of the absolute deviations from the mean.
In a box plot, if the median is in the center of the box and the left and right whiskers are equidistant from their respective quartiles, then the distribution is
symmetric
The pth percentile is the value
that has p% of the values below it.
If Lp for a given percentile equals 12, then the percentile is
the 12th smallest value.
The arithmetic mean is usually NOT a good measure of central location if
the data contains an outlier(s). Reason: Data outliers can skew the mean to be either smaller or greater than typical values.
The median is defined as
the middle value of a data set
The mode is defined as
the most frequently occurring value of a data set.
Nadia purchased 200 shares of XYZ stock at $20 per share. When the stock decreased in value to $15 a share, Nadia purchased 300 more shares of XYZ stock. When calculating the weighted average price per share, the weights are
the numbers of shares purchased at each price.
Two widely used measures of dispersion are
the variance and the standard deviation.
A positive z-score indicates that the sample value is
to the right of the mean.
True or false: For a population, the coefficient of variation (CV) is calculated as σ/μ.
true
All of the following are measures of central location EXCEPT the ______.
variance Reason: The variance measures the dispersion or the spread of the data, not the central location.
When a mean is calculated and some observations are given greater importance than others, we refer to this measure of central location as a ______.
weighted mean
Grades in a particular statistics class are based on homework, a midterm exam, and a final exam. The homework is 20% of the final grade. The midterm and final are each 40% of the final grade. What measure should be used to calculate final course grades?
weighted mean NOT Arithmetic Mean Reason: This is used when each grade counts the same.
Chebyshev's theorem is applicable
when the data have any shape.
Which one of the following z-scores indicates that an observation is an outlier?
|z| > 3
