What are quantiles and quartiles?

easy

Answer

$The q-quantile is the value below which fraction q of the data falls.$
$Median = 0.5-quantile.$
$Quartiles: Q1 (0.25), Q2 (0.5, median), Q3 (0.75).$
$Interquartile range IQR = Q3 - Q1.$
$Used for robust spread measurement, boxplots, outlier detection (points > Q3 + 1.5\cdotIQR or < Q1 - 1.5\cdotIQR are 'outliers' by Tukey's rule).$
$Y \mid X$

Check yourself — multiple choice

Only mean and variance matter
q-quantile: fraction q below; IQR = Q3-Q1; outlier rule: Q1 - 1.5·IQR or Q3 + 1.5·IQR; foundation of quantile regression
Same as mean
Not robust

Quantiles + IQR: robust spread; Tukey outlier rule; quantile regression.

#descriptive

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