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Measures of center
mean & median
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Mean
- symmetrical distribution, arithmetic average, influenced by skew and outliers
- For symmetrical distribution, the mean and median will be the same
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Median
skewed distribution , midpoint of a distribution, resistant to skew and outliers
For skewed distribution, the mean is influenced by extreme observations
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Measures of spread
Quartiles & Standard Deviation
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Quartiles
skewed distribution
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First Quartile
value in the sample that has 25% of the data at or below it
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Third Quartile
value in the sample that has 75% of the data at or below it
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Interquartile range
(IQR) = Q3 - Q1
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Outlier
an individual value that falls outside the overall pattern.
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Low outlier:
any value < (Q1 – 1.5 IQR)
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High outlier
any value > (Q3 + 1.5 IQR)
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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
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Statistical Summary
Symmetrical distribution & Skewed distribution
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Symmetrical distribution
mean and standard deviation
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Skewed distribution
- five number summary, boxplot
- [Minimum, Q1, M, Q3, Maximum]
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