How to get frequencies for 5 points summary values?

[#1]

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... 

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)

[#2]

Hi Neo,

In this example, the frequencies are derived from your observations (i.e., user-defined). In other words, Frequencies are the input, not the output.

For your specific case, I don't believe that JMP offers an easy way to plot aggregated data in the format you described. Still, others may have an elegant solution to your problem.

Best,

TS

[#3]

@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

txnelson_0-1706717700286.png

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;

[#4]

@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.

[#5]

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.