business stats ch3

Which of the following statements regarding the geometric mean is MOST accurate? The geometric mean is less sensitive to extreme values than the arithmetic mean. The geometric mean return is a better measure than the arithmetic mean return when considering an investment over a single time period. Two mathematical steps are needed to calculate the geometric mean: Addition and Division.

The geometric mean is less sensitive to extreme values than the arithmetic mean.

Which of the following statements about variance is the most accurate? Variance is the square root of the standard deviation. Variance can be both, positive or negative. Variance is denominated in the same units as the original data. Variance is the average of the squared deviations from the mean.

Variance is the average of the squared deviations from the mean.

The arithmetic mean ignores the effects of

compounding

describes only the direction of the linear relationship between two random variables.

covariance

The correlation coefficient...

describes both the direction and the strength of the linear relationship between two random variables. Values fall between -1 (negative relationship) +1 (positive relationship), and 0 (no relation). Calculated as: the Covariance of two variables divided by the product of their Standard Deviations.

For a symmetric and unimodal distribution, the mean, the median, and the mode are

equal

true or false: The geometric mean return is a better measure than the arithmetic mean return when considering an investment over a single time period.

false The geometric mean is more appropriate than the arithmetic mean when tracking investment returns over several time periods.

The appropriate measure for evaluating investment returns over several years is the...

geometric mean

geometric mean

is a multiplicative average. - Smaller than the arithmetic mean - Less sensitive to outliers Relevant measure when evaluating investment returns over several years - Calculating the average growth rates

arithmetic mean

is additive. - Ignores the effects of compounding - Suitable for analyzing a one-year investment

The advantage of using mean absolute deviation rather than variance as a measure of dispersion is that mean absolute deviation __________. Multiple Choice is less sensitive to extreme deviations Correct requires fewer observations to be a valid measure is a relative measure rather than an absolute measure of risk considers only unfavorable (negative) deviations from the mean

is less sensitive to extreme deviations

A negative skewness coefficient implies that extreme observations are concentrated in the tail of the distribution.

left

A ___ for the standard deviation indicates that the data points are close to the mean, while a ___ for the standard deviation indicates that the data are spread out.

low, high

We interpret the geometric mean return as the ____return that you will earn from an investment.

mean

The average of the absolute differences between the values of the data set and the mean is the

mean absolute deviation.

We refer to the arithmetic mean as simply the _____ or the _____

mean or the average

empirical rule applies to

relatively symmetric and bell shaped data

s^2

sample variance

The empirical rule is appropriate when the distribution of a variable is _____ and _____ -shaped

symmetric, bell

The function to find the mean of a subset in R is

tapply

Two widely used measures of dispersion are...

the variance and the standard deviation.

The formula for the weighted mean is xx=Σwixi. Using this formula, what is the restrictions on the weights.

they must sum to one

The Z-score is a ____ measure

unitless

Which of the following is not a measure of central location? mode median mean weighted mean variance

variance

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 The weights represent the relative importance!

relative location

where a place is located in relation to another place

-score to find the relative position of an observation within a distribution

z

is a visual representation of particular percentiles.

boxplot

relates to the way data tend to cluster around some middle or central value

central location

What is the difference between Chebyshev's Theorem and the Empirical Rule?

Chebyshev's theorem applies to all data sets, whereas the empirical rule is only appropriate when the data have approximately a symmetric and bell-shaped distribution.

In a box plot, if the median is left of center and the right whisker is longer than the left whisker, then the distribution is...

negatively skewed

A z-score larger than 3 or less than -3 indicates a/n

outlier

The pth percentile divides a variable into two parts. What percentage is less than p?

p

The notation μ represents the

population mean

The average of the sum of squared differences from the mean is the

population variance

Place the steps for constructing a boxplot to find outliers in the correct order.

1. plot five-number summary values in ascending order on the horizontal axis 2. draw a box encompassing the first and third quartiles 3. draw a dashed vertical line in the box at the median 4. calculate the difference between q3 and q1. 5. use an asterisk to indicate points that are farther than 1.5 x IQR from the box

The empirical rule states that approximately ___% of observations will fall within three standard deviations of the mean

100

coefficient of variation is calculated as the

Std. Dev. divided by the Mean

Place in order, from beginning to end, the steps to calculate the mean absolute deviation.

1. calculate arithmetic mean for the data set 2.find the absolute difference between each value and the mean 3. sum the absolute differences 4. divide by the sample (or the population) size.

The empirical rule states that approximately ___% of observations will fall within one standard deviation of the mean

68

The empirical rule states that ___% of observations will fall within two standard deviations of the mean.

95

The function to find the mean of a subset in Excel is

=AVERAGEIF

function for sample correlation cofficient

=correl

function for sample covariance

=covariance.s

Which of the following relationships cannot be concluded from examining the correlation coefficient? No relationship A positive relationship A curvilinear relationship Correct A negative relationship

A curvilinear relationship

When interpreting the covariance between variables x and y, which of the following statements is the most accurate?

A positive value of covariance indicates that, on average, if x is above its mean, then y tends to be above its mean.

Which of the following statements is most accurate when defining percentiles?

Approximately (100 − p)% of the observations are greater than the pth percentile.

Which of the following is the most influenced by outliers? Multiple Choice Mode Median 75th percentile Arithmetic mean

Arithmetic mean

In what way(s) is(are) the concept of geometric mean useful? In evaluating investment returns In calculating average growth rates In assessing the dispersion of the data Both in evaluating investment returns and in calculating average growth rates

Both in evaluating investment returns and in calculating average growth rates

What is(are) characteristic(s) of the geometric mean? Multiple Choice It is always greater than the arithmetic mean. It is the mathematical equivalent to the median. It is always less than or equal to the arithmetic mean. Correct Both it is the mathematical equivalent to the median and it is always less than or equal to the arithmetic mean

It is always less than or equal to the arithmetic mean.

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

Which of the following are included in a five-number summary?

The minimum value Q2 The maximum value Q1 Q3

what values are used in a box plot

The only values used are the minimum, Q1, median, Q3, and the maximum.

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 capabilities does Analysis of Relative Location provide? Multiple Choice They make statements regarding the shape of the data. They make statements regarding the central location of the data. They make statements regarding the dispersion of the data around the median. They make statements regarding the percentage of data values that fall within some number of standard deviations from the mean.

They make statements regarding the percentage of data values that fall within some number of standard deviations from the mean.

true or false: Two mathematical steps are needed to calculate the geometric mean: Addition and Division.

Those steps apply to the arithmetic mean. The geometric mean involves: Multiplication and taking nth roots.

A box-and-whisker plot is another name for a

boxplot

Is it possible for a data set to have more than one mode?

Yes, if two or more values in a data set occur with the most frequency and the frequency is greater than one.

The coefficient of variation is BEST described as

a relative measure of dispersion.

Chebyshev's theorum

applies to any data shape

The _____ and the _____ are the most extensively used measures of central location and dispersion, respectively.

mean, standard deviation

Generally, the ___ is the best measure of central location when outliers are present.

median

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 geometric mean arithmetic mean mode

median

is a measure of central location that divides the observations for a variable in half.

median

what symmetry box plot looks like

median is in the center of the box, and the left and right whiskers are equally distant from their respective quartiles

positively skewed

median is left of center and the right whisker is longer than the left whisker

Negatively skewed

median is right of center and the left whisker is longer than the right whisker

When summarizing a qualitative data set, the ______ is the best measure of central location.

mode