How to get frequencies for 5 points summary values?

Question

I am struggling to understand how the frequency values are obtained in this example (5% and 95 % quantiles assumed).

https://community.jmp.com/t5/JSL-Cookbook-Archived/Create-a-Box-Plot-from-a-Five-Number-Summary/ta-p/41278

How would the values change if I have 25% and 75% quantile values?

(In my case, I will have Min, Q1 (25%), Median, Q3 (75%) and Max values)

dlehman1 · Answer

Since the first quartile contains 25% of the data, wouldn't you just multiply your total number of data points by .25 to get the frequency for that quartile.  And so on.  I think that if you have the 5 point summary and know the total number of data points, that is how to create the frequency column.  I can't think of any other way and I believe the 5 point summary alone cannot give you the frequencies - you need at least one other piece of information.

Neo · Answer

@txnelson I am looking to generate the frequency column. I already have the 5 point summary column and I know which values are my Min, Q1 (25% quantile), Median, Q3 (75% quantile) and Max.

txnelson · Answer

@Neo

Are you looking for how to handle such a distribution in Open code?  If so, below is one way to handle it.

Given the Boxplot data table, from the referenced link

The following JSL will produce the correct quantiles thru expansion into a matrix

Names Default To Here( 1 );
dt = Data Table( "Boxplot" );
a = [];
For Each Row( a = a |/ Repeat( dt:Summary Point[Row()], dt:Freq[Row()] ) );
Show( Quantile( .05, a ), Quantile( .95, a ) );

resulting in

Quantile(0.05, a) = 3;
Quantile(0.95, a) = 42;