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3.Numerical Descriptive Measures (3.2 Variation and Shape (Shape:Skewness,…
3.Numerical Descriptive Measures
3.1
Central Tendency
-the extent to which the values of a numerical variable group around a typical,or central,value
The median=(n+1)/2 ranked value
The mode-多个或者无
The mean
The geometric mean
3.2
Variation and Shape
Z scores
Coefficient of variation
Sample standard deviation
Sample ariance
The range=X largest- X smallest
Shape:Skewness
Mean=median:symmetrical distribution
Mean>median:positive,right-skewed distribution
Mean<median:negative,left-skewed distribution
Shape:kurtosis
Lepokurtic-higher concentration
Platykurtic-lower concentration
3.3 Exploring Numerical Data
The interquartile range=Q3-Q1
（not influenced by extreme values)
resistant measures-median,Q1,Q3,ir
the five-number summary
X smallest, Q1, median, Q3, X largest
p140 table3.5
Quartiles
second quartile(Q2)
third quartile(Q3)=3(n+1)/4ranked value
first quartile(Q1)=(n+1)/4ranked value
the boxplot
3.4 Numerical Descriptive Measures for a population
The population variance and standard deviation
The empirical rule: 68%+-1, 95%+-2, 99.7%+-3
Population mean
Chebyshev's theorem
The covariance and the coefficient of correlation