Our World Statistics Day conversations have been a great reminder of how much statistics can inform our lives. Do you have an example of how statistics has made a difference in your life? Share your story with the Community!
Choose Language Hide Translation Bar

## Problem

Instead of a full data set, you have a summarized version that contains the five numbers needed to define a box plot.

## Solution

You can use frequencies to mimic a full data set based on the five-number summary. If you enter the five data points in a data table and then create a second column with frequencies that force your data points to be at the appropriate quantiles, you can use that data table as if it were the raw data. For a box plot with endpoints at the 5% and 95% quantiles, you could use the five-point summary 3, 15, 20, 40, 42 with frequencies of 5, 20, 25, 25, and 20, respectively. The following JSL gives an example:

``````Names Default To Here( 1 );
dt = New Table( "Boxplot",
New Column( "Summary Point",
Numeric,
"Continuous",
Format( "Best", 18 ),
Set Values( [3, 15, 20, 40, 42] )
),
New Column( "Freq",
Numeric,
"Continuous",
Format( "Best", 18 ),
Set Values( [5, 20, 25, 25, 20] )
)
);

dt << Graph Builder(
Variables( Y( :Summary Point ), Frequency( :Freq ) ),
Elements( Box Plot( Y, Legend( 7 ) ) )
);``````

## Discussion

The summarized values above are for illustration purposes and can be replaced by other values.