chapter 3 unit c e280
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Arithmetic mean
 is a primary measure of central location (Average)
 the mean is sensitive to outliers

median (when outlier affect the mean , median can better indicator of the center of the data)
 is another measure of central location
 when data are arranged in ascending order. the median is: the middle value is the number of observations is odd or the average of the two middle values if the number of observation is even

mode
most frequently occurring value in a data set, a data set can have no modeĀ one mode of many modes

five number summary
 S=smallest value=min
 Q1=1 quartile=25 percentile
 Q2=median=50 th
 Q3=3 quartile=75 percentile
 L=largest=max

range
interquartile range
 range= Largestsmallest=the number of units within which all of the data exist
 interquartile range =Q3Q1=the number of units within which the middle 50 % of data exist

box and whisker plot
you graphically display information from the 5 number summary

Mean Absolute Deviation (MAD)
is an average of the absolute difference of each observation from the mean

Variance and standard deviation
the most commonly used measures of dispersion

Coefficient of variation (cv)
 cv adjust for differences in the magnitudes of the means
 cv is unitless, allowing easy comparisons of meanadjusted dispersion across different data sets

Chebyshev's theorem
 for anydata set, the proportion of observations that lie within k standard deviations from the mean is at least 1a/k^{2},where k is any number greater than 1
 applies to all data sets
 for k=2 standard dev 75%
 for k=3 standard dev 89%

the Empirical Rule
 applies to data sets that are relatively symmetric and bellshaped
 1 standard dev = 68%
 2 standard dev =95%
 3 standard dev = 99.7 %

Covariance
describes the direction of the linear relationship between two variables

correlation coefficient
 describes both the direction and strength of the relationship between x and y
 closer 1, stronger negative linear
 closer to+1. stronger positive linear
 closer to 0, the weaker the linear relationship