Quantiles Michele Stora. Quantiles ► one of the class of values of a variate that divides the total frequency of a sample or population into a given number.

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Presentation transcript:

Quantiles Michele Stora

Quantiles ► one of the class of values of a variate that divides the total frequency of a sample or population into a given number of equal proportions ► The n-1 variate values which divide the total frequency into n equal parts. ► Examples:  Percentile  Decile  Quartile  Quintile

Quantiles ► The 100-quantiles are called percentiles. ► The 10-quantiles are called deciles. ► The 5-quantiles are call quintiles. ► The 4-quantiles are called quartiles.

Percentiles ► The kth percentile is a scale value for a data series equal to the p/100 quantile ► The 1st percentile cuts off lowest 1% of data ► The 98th percentile cuts off lowest 98% of data ► The 25 th percentiles is the first quartile ► The 50 th percentile is the median

Deciles ► Represents 1/10 of the total population ► The 1 st decile cuts off the lowest 10% of data ► The 9 th decile cuts off the lowest 90% of data

Quartiles ► The quartiles divide the distribution into four equal parts  called fourths  The total of 100% is broken into four equal parts: 25%, 50%, 75%, 100%.  The total of 100% is broken into four equal parts: 25%, 50%, 75%, 100%. ► Lower Quartile is the 25th percentile. (0.25) ► Median Quartile is the 50th percentile. (0.50) ► Median Quartile is the 50th percentile. (0.50) ► Upper Quartile is the 75th percentile. (0.75)

Quintiles ► Represents 20% or 1/5 of the given amount

Box Plot ► A visual tool that illustrates the distribution of a univariate dataset. ► It illustrates the median, upper and lower quantiles, upper and lower deciles, and any outliers.

Box Plot