

How many seeds does a pomegranate have?
AND
Does a larger pomegranate yield proportionally more seed volume?
Pomegranates are curious fruits  applesized, red in color, and containing hundreds of pitchred juicy seeds. Bittersweet in taste, depending on ripeness, puts these delightful transparent fragilities inbetween grapefruits and red grapes.


Figure 1.1 Click image to enlarge, or click here to open


What has nature blessed us with  the pomegranate is a very unstructured structured fruit. It contains multiple compartments, each tightly packing seeds around a spongelike center, in some more or less random formation.


Figure 1.2 Click image to enlarge, or click here to open


Sources are in disagreement about how many seeds a pomegranate holds. Some sources fix the number to exactly 613, some allow for an error of +/ 200, yet others believe that all pomegranates have the exact same number of seeds. It is certainly possible to disprove the first and third of these.


Figure 1.3 Click image to enlarge, or click here to open


Then how many seeds are in a typical pomegranate? Here we keep track of a very small number of pomegranates, carefully disected and accounted for. This is an ongoing experiments, and depending on mood and taste buds, the table will be filled with additional pomegranates.


Figure 1.4 Click image to enlarge, or click here to open


Next to the number of seeds in a pomegranate, another phenomena is its highly varying size. Does size matter? We assume that a larger pomegranate yields proportionally more seed volume, but this is not quite true.
Recently, we have begun annotating our new additions to the dataset with data for volume. For each new pomegranate, we measure its total volume, and, after careful counting of seeds, we measure the total seed volume. The plotted and curvefit data shows that with increasing total volume (which is highly correlated to weight), the volume of extracted seeds grows logarithmically. That is, seed volume grows only marginally with size and weight. While the dataset is still small, the computed logarithmic curve fits to the dataset with a relatively small error (Rsquared tends towards 1).
These results are not surprising. When comparing the amount of pulp in a large pomegranate to that of a small one, you will notice that the shell of a large pomegranate is significantly thicker.
Country 
Sample Size 
min #seeds 
max #seeds 
avg #seeds 
min weight (g) 
max weight (g) 
avg weight (g) 
US 
150 
286 
1370 
680 
145 
1065 
421 
Singapore 
2 
339 
579 
459 
250 
400 
325 
Iran 
37 
165 
1263 
338 
200 
660 
354 
Spain 
2 
580 
837 
709 
280 
330 
305 
Turkey 
12 
267 
971 
576 
226 
1001 
603 
Brazil 
3 
647 
1054 
809 
568 
658 
599 

All 
206 
165 
1370 
613 
145 
1065 
420 

Table 1.1: Pomegranate Statistics (download the data file for a complete listing of each pomegranate)

Download the Matlab code for the distribution shown in Figures
1.5 and 1.6. All three files are required.
Pomegranates of different sizes and origins have a highly varying number of seeds. Pomegranates from Iran tend to be small, but have very large and sweet seeds. Pomegranates from the U.S. come in all sizes and their seeds can be anywhere from bitter to sweet. With increasing number of seeds per pomegranate, size and weight per seed decreases. The relationship can at best (low R^{2} value) be described as an inverse relationship. (see Figure
1.5)

Figure 1.5: Distribution of weight and seed count by country of origin 
With increasing size and weight of a pomegranate, the volume of seeds grows only marginally. This relationship can be well described (high R^{2} value) by a logarithmic function. (see Figure
1.6)

Figure 1.6: Distribution of weight and volume by country of origin 

