Ch. 3 LearnSmart

place in order, from beginning to end, the steps to calculate the mean absolute deviation. a. sum the absolute differences b. find the absolute difference between each value and the mean c. divide by the sample (or the population) size d. calculate the arithmetic mean for the data set

d. calculate the arithmetic mean for the data set b. find the absolute difference between each value and the mean a. sum the absolute differences c. divide by the sample (or the population) size

for a symmetric and unimodal distribution, the mean, the median, and the mode are ____________

equal

true or false: mean-variance analysis suggests that investments with lower average returns are also associated with higher risks.

false

quartiles divide the data into ______ equal parts.

four

the ______ is the multiplicative average of a data set.

geometric mean

the appropriate measure for evaluating investment returns over several years is the... a. geometric mean b. mode c. median d. arithmetic mean

geometric mean

when calculating average growth rates, we apply the formula for the...

geometric mean

match these quartiles with their percentiles. i.) Q1 ii.) Q2 iii.) Q3 iv.) Q4

i.) Q1 = 25th percentile ii.) Q2 = 50th percentile iii.) Q3 = 75th percentile iv.) Q4 = 100th percentile

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

left

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

low; high

what is the most widely-used measure of central location?

mean

the ______ measures the difference between the largest and smallest values in a data set.

range

the ___________ is not considered a good measure of dispersion because it focuses solely on the extreme values and ignores every other observation in the sample or the population.

range

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 notation (bar above x) represents the ______.

sample mean

the empirical rule is appropriate when the distribution of a variable is __________ and ____________-shaped. (Enter one word in each blank.)

symmetric and bell-shaped

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

tapply

when there are an even number of observations, and the observations are in order from smallest to largest, the median is...

the average of the two middle observations

which of the following values is included in a box plot?

the first quartile

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 mean

when there are an odd number of observations, and the observations are in order from smallest to largest, the median is...

the middle observation

the median is defined as

the middle value of a data set

which of the following values is included in a box plot?

the second quartile

what is the relationship between the variance and the standard deviation?

the standard deviation is the positive square root of the variance

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 mode's usefulness as a measure of central location tends to diminish with variables that have more than _____________ modes.

three

true or false: the empirical rule should be applied to data sets that are approximately bell-shaped.

true

true or false: the mean is the most widely used measure of central location for quantitative data.

true

if a variable has one mode, then we say it is __________

unimodal

which of the following is not a measure of central location?

variance

a ____________ mean is used to calculate the mean of a frequency distribution.

weighted

is it possible for a data set to have NO mode?

yes, if there are no observations that occur more than once

a ___________ helps us identify outliers and skewness in the distribution of a variable.

boxplot

a _____________ is a visual representation of particular percentiles.

boxplot

the term ____________ ___________ relates to the way data tend to cluster around some middle or central value.

central location

the arithmetic mean is usually NOT a good measure of central location if a(n) ______ exists.

outlier reason: data outliers can skew the mean to be either smaller or greater than typical values

the notation μ represents the ______.

population mean

if the covariance between two random variables x and y is positive, then x and y have a(n) _____.

positive linear relationship

the mean is usually greater than the median when the data are ____________ skewed.

positively

henry's score on an accounting exam placed him in the 85th percentile in the class. what percentage of students scored higher than Henry?

15%

if the median price for a home is $200,000, then ______ of the homes cost less than $200,000.

50%

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

68%

the empirical rule states that approximately __________% 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(range, criteria, [average_range])

which of the following statements about the mean absolute deviation (MAD) is MOST accurate?

MAD is denominated in the same units as the original data

in which of the following data sets would the arithmetic mean NOT be a good measure of central location? a. 7, 8, 8, 9, 25 b. 2, 3, 4, 4, 5 c. 6, 7, 7, 8, 8 d. 5, 5, 6, 6, 7

a. 7, 8, 8, 9, 25

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

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

the pth percentile divides a variable into two parts. what percentage is less than the pth percentile?

approximately p percent

the owner of BevaMart wants to study the relationship between the outside temperature and hot chocolate sales. the owner computed the covariance between outside temperature and hot chocolate sales 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

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

mean, standard deviation

Rate of return is evaluated in terms of its reward (________) and risk (________).

mean; variance

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

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

if a variable has two modes, then we say it is __________

multimodal