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Measures of center
mean & median

Mean
 symmetrical distribution, arithmetic average, influenced by skew and outliers
 For symmetrical distribution, the mean and median will be the same

Median
skewed distribution , midpoint of a distribution, resistant to skew and outliers
For skewed distribution, the mean is influenced by extreme observations

Measures of spread
Quartiles & Standard Deviation

Quartiles
skewed distribution

First Quartile
value in the sample that has 25% of the data at or below it

Third Quartile
value in the sample that has 75% of the data at or below it

Interquartile range
(IQR) = Q3  Q1

Outlier
an individual value that falls outside the overall pattern.

Low outlier:
any value < (Q1 – 1.5 IQR)

High outlier
any value > (Q3 + 1.5 IQR)

Standard Deviation
 (s) – symmetrical distribution
 Variation around the mean, how spread out from the mean the data is
 When s = 0 : no spread in the data
 As s increases, the data is more widely spread around the mean

Statistical Summary
Symmetrical distribution & Skewed distribution

Symmetrical distribution
mean and standard deviation

Skewed distribution
 five number summary, boxplot
 [Minimum, Q1, M, Q3, Maximum]

