QM 214 - Chapter 3

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outliers

extremely small or large variables

the 25th percentile is referred to as:

first quartile (Q1)

the median is especially (useful/useless) when outliers are present

useful

in order to return to the original units of measurement, we take the positive square root of ________, which gives us the standard deviation

variance

the ___________ is defined as the average of the squared differences between the observation and the mean

variance

two most widely used measures of dispersion:

variance and standard deviation

the ________ ________ is relevant when some observations contribute more than others

weighted mean

the mean of the sample (sample mean) is referred to as:

x̅ (x-bar)

sample mean formula:

x̅ = ( Σ xi ) / n -all that formula is saying is add up all of the numbers in your data set ( Σ means "add up", xi means "all the numbers in the data set, and n is # of items in the sample)

weighted mean formula (sample):

x̅ = Σwi*xi

the mean of the population (population mean) is referred to as:

μ

population mean formula:

μ = ∑*X / N -all that formula is saying is add up all of the numbers in your data set (Σ means "add up", xi means "all the numbers in the data set, and N is # of items in the population)

in general, the pth percentile divides a data set into two parts:

- approximately p percent of the observations have values less than the pth percent - approximately (100-p) percent of the observations have values greater than the pth percentile

the median is also known as the ______ percentile

50th

locate approximate position of the percentile by calculating Lp:

Lp = (n+1)*P/100

we calculate the median as the average of the two middle values if the number of observations is _______

even

mean absolute deviation (MAD)

an average of the absolute differences between the observations and the mean

to calculate a percentile, first arrange the data in ________ order

ascending (smallest to largest)

we arrange the median data in __________ order from ______ to ________.

ascending / smallest / largest

a _______ ______ is (more or less) a visual representation of particular percentiles

box plot

a _______ _______ is a convenient way to graphically display the minimum value (Min), the quartiles (Q1, Q2, Q3), and the maximum value (Max) of a data set

box plot

a unitless measure that allows for direct comparisons of mean-adjusted dispersion across different data sets

coefficient of variation (CV)

unimodal

data set has one mode

bimodal

data set has two modes

multimodal

data set has two or more modes

calculating coefficient of variation (CV):

dividing a data set's standard deviation by its mean

if Lp is an ______ then Lp denotes the location of the pth percentile

integer

if Lp is not an integer, we need to _________ between two observations to approximate the desired percentile

interpolate

population CV formula

look it up

population MAD formula

look it up

population standard deviation formula

look it up

population variance formula

look it up

sample CV formula

look it up

sample MAD formula:

look it up

sample standard deviation formula

look it up

sample variance formula

look up

the range is the difference between:

maximum (Max) and minimum (Min) Max - Min = Range

the _______ is the most commonly used measure of central location

mean

the _______ divides the data in _____. an equal number of observations lie above and below the _________

median / half / median

the __________ is the only meaningful measure of central location in qualitative data, as opposed to quantitative data

mode

if the median is right of center and the left whisker is longer than the right whisker, then the distribution is

negatively skewed

we calculate the median as the middle value if the number of observations is _______

odd

variance squares the __________ units of measurement

original

if the values of the mean and median differ significantly, it is likely that the data set contains ___________

outliers

one weakness of the mean is that it is unduly influenced by __________

outliers

we refer to the population mean as a _______ and the sample mean as a _______ since the population mean is generally unknown and the sample mean is used to estimate it.

parameter / statistic

_________ provide detailed information about how data are spread over the interval from the smallest value to the largest value

percentiles

if the median is left of center and the right whisker is longer than the left whisker, then the distribution is

positively skewed

arithmetic mean

primary measure of central location. the mean/average. -add up values of all data points and divide by number of data points in population/sample

the ________ is not considered a good measure of dispersion because it focuses solely on the extreme values and ignores every other observation in the data set

range

the simplest measure of dispersion

range

n indicates:

sample size (for population percentile, replace n with N)

the 50th percentile is referred to as:

second quartile (Q2)

coefficient of variation (CV)

serves as a relative measure of dispersion and adjusts for differences in the magnitudes of the means

interquartile range (IQR)

the difference between the first and third quartiles IQR = Q3 - Q1

Lp indicates:

the location of the desired pth percentile

median

the middle value of a data set

mode

the most frequently occurring value in a data set. a data set may have no mode or more than one mode

central location

the way quantitative data tend to cluster around some middle or central value. measures of central location attempt to find a typical or central value that describes the data

the 75th percentile is referred to as:

third quartile (Q3)

the mode's value as a measure of central location tends to diminish with data sets that have more than ______ modes

three


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