BoxChart goes below 0 although min value is > 0

[beatngu13]

MWE:

final BoxChart chart = new BoxChartBuilder().build();
chart.addSeries("seriesName", List.of(1_000, 5_000, 60_000));
new SwingWrapper(chart).displayChart();

Creates the following chart:

As can be seen in the code example, the min value is 1,000, but the boxplot goes below 0.

Is this a config issue or a bug?

[Mr14huashao]

@beatngu13
The calculation formula is as follows，and you can see readme.md
Q1 = 1000
Q2 = 5000
Q3 = 60000
Upper limit = Q3 + 1.5 * IQR = Q3 + 1.5 *(Q3 - Q1)
Lower limit = Q1 - 1.5 * IQR = Q1 - 1.5 *(Q3 -Q1) = -81500
so the boxplot goes below 0

[beatngu13]

Hey @Mr14huashao,

Thanks for pointing to the underlying formula. I already had a quick look at it, but is the calculation correct this way?

AFAIK boxplots are based on the five-number summary, why should the lower limit be less than the minimum?

If I go to e.g. this online calculator and use the example dataset (1000, 5000, 60000), I get:

• Minimum: 1000
• Quartile Q1: 3000
• Quartile Q2 (median): 5000
• Quartile Q3: 32500
• Maximum: 60000

Then the lower fence (not limit?) should be:

Lower fence = Q1 - 1.5 * IQR
            = Q1 - 1.5 * (Q3 - Q1)
            = 3000 - 1.5 * (32500 - 3000)
            = 3000 - 1.5 * 29500
            = -41250

Since there are no outliers, the lower and upper limits should correspond to the minimum and maximum values I would say.

Also, if you use other online chart makers, you get different results. For example, plot.ly:

Or BoxPlotR:

[Mr14huashao]

@beatngu13 can you spare me a few minutes to see this issue?

[beatngu13]

@Mr14huashao sure, how can I help?

[Mr14huashao]

@beatngu13
I have found the problem and I will fix it.

[timmolter]

@Mr14huashao Thanks!

BTW, the original inspiration for this was MATLAB: https://www.mathworks.com/help/stats/boxplot.html

[Mr14huashao]

@timmolter
To calculate the quartile, there are several ways to calculate the position of Qi:

• “n + 1”: determine the position of the quartile, where Qi is = i (n + 1) / 4, where i = 1, 2, and 3. n represents the number of items contained in the sequence.
  Calculate the corresponding quartile based on location
• “n-1”: Determine the position of the quartile, where Qi is = i (n-1) / 4, where i = 1, 2, and 3. n represents the number of items contained in the sequence.
  Calculate the corresponding quartile based on location
• “np”: Determine the position of the quartile, where Qi is np = (i * n) / 4, where i = 1, 2, and 3. n represents the number of items contained in the sequence.
  If np is not an integer, Qi = X [np + 1]
  If np is an integer, Qi = (X [np] + X [np + 1]) / 2
• “(n-1) / 4 +1”: Determine the position of the quartile, where Qi is = i (n-1) / 4 + 1, where i = 1, 2, 3. n represents the number of items contained in the sequence.
  Calculate the corresponding quartile based on location

Example:
An example of a set of sequence numbers: 12, 15, 17, 19, 20, 23, 25, 28, 30, 33, 34, 35, 36, 37

• Method 1:
  Q1's position = (14 + 1) /4=3.75,
  Q1 = 0.25 × third term + 0.75 × fourth term = 0.25 × 17 + 0.75 × 19 = 18.5;
• Method 2:
  Q1's location = (14-1) /4=3.25,
  Q1 = 0.75 × third term + 0.25 × fourth term = 0.75 × 17 + 0.25 × 19 = 17.5;
• Method 3:
  Q1's position = 14 * 0.25 = 3.5,
  Q1 = 19;
• Method 4:
  Q1's location = (14-1) / 4 + 1 = 4.25
  Q1 = 0.75 × the fourth term + 0.25 × the fifth term = 0.75 × 19 + 0.25 × 20 = 19.25.

Are all four calculation methods implemented?

[beatngu13]

Thanks for the quick fix! 🙏