Summary Analysed coins Analysis

Summary

Third staters can be divided into two groups. The first consists of Types 4.1–2 and 4.5 (Group 4A), and the second of Types 4.3–4 and 4.6–10 (Group 4B), with the second group characterised by a slightly lower weight standard and, at the same time, a greater dispersion of coin weights. The difference in the average observed weights of these two groups is 0.09 g, and the difference in medians is 0.07 g, representing a decrease of 1.6% and 2.0%, respectively. However, due to the small number of observations, this segmentation of third staters cannot be considered completely certain or the only possible one, and a larger sample is needed to confirm or refine it.

Analysed coins

Coin catalogue section:	Kelenderis
Coin corpus datasets:	Kelenderis, Third staters

The numbers of analysed coins are given in Table 1. Coins whose weight is unknown or unreliable, or that are excessively corroded or damaged, are excluded from the analysis.

Corpus	Number of coins as of 1 November 2025
	Total	Excluded	Analysed
Kelenderis, Third staters	36	2	34

Table 1: Numbers of analysed coins

Analysis

Box plots1 of individual coin types and basic descriptive statistics are presented in Figure 1 and Table 2 (Std. Dev. denotes the standard deviation and IQR the interquartile range), respectively.

Figure 1: Box plots of individual coin types

Type	Count	Mean	Median	Std. Dev.	IQR
4.1	1	3.59	3.59
4.2	5	3.55	3.56	0.04	0.07
4.3	3	3.52	3.50	0.04	0.05
4.4	7	3.48	3.50	0.09	0.14
4.5	1	3.56	3.56
4.6	3	3.47	3.46	0.08	0.12
4.7	2	3.52	3.52	0.09	0.13
4.8	10	3.49	3.49	0.09	0.10
4.9	1	3.48	3.48
4.10	1	3.49	3.49

Table 2: Basic descriptive statistics of coin types

As Figure 1 and Table 2 show, the weight standard of Types 4.1, 4.2 and 4.5 appears to be higher than that of the other types. Third staters can therefore be divided into the following two groups:

Group 4A:	Types 4.1–2; and 4.5
Group 4B:	Types 4.3–4 and 4.6–10.

However, due to the small size of the data sample, this segmentation is still preliminary. Note, for example, that the weights of two coins of Type 4.8 exceed the highest weight observed in Group 4A. These are coins Ref. Nos. KE4029 and KE4032 weighing 3.64 g and 3.62 g, respectively, while the heaviest coin of Group 4A weighs 3.61 g (coin Ref. No. KE4006). Perhaps this can be explained by the fact that less attention was paid to the weight of the flans of this type.

Table 3 shows the descriptive statistics of all third staters and of Groups 4A and 4B.

Statistics	All coins	Group 4A	Group 4B
Number of coins:	34	7	27
Mean:	3.50	3.56	3.49
Standard deviation:	0.07	0.04	0.08
Interquartile range:	0.09	0.06	0.10
Skewness:	-0.38	-0.21	-0.11
Kurtosis:	2.67	1.86	2.65
Minimum:	3.34	3.51	3.34
25th percentile:	3.47	3.52	3.45
Median:	3.50	3.56	3.49
75th percentile:	3.56	3.58	3.55
Maximum:	3.64	3.61	3.64

Table 3: Descriptive statistics of coin groups

The following charts visualise the weight distributions of these groups. Figure 2 shows box plots and Figure 3 presents relative frequency histograms (the bars represent the relative frequencies of observations ranging from 3.30 to 3.65 g in increments of 0.05 g). The continuous curves represent approximations of the data by the Weibull distribution2 based on maximum likelihood estimates. Cumulative distributions are shown in Figure 4.

Figure 2: Box plots of Groups 4A and 4B

Figure 3: Relative frequency histograms of Groups 4A and 4B

Figure 4: Cumulative distributions of Groups 4A and 4B

The two-sample Kolmogorov-Smirnov test rejects the hypothesis that the weight distributions of Groups 4A and 4B are equal (p-value of 0.013). Similarly, the one-sided Welch’s t-test3 rejects the null hypothesis that the mean weights of both groups are equal in favour of the alternative that the mean weight of Group 4A is higher than that of Group 4B (p-value of 0.002). The percentile bootstrap method was also used to supplement these results. Table 4 shows the observed sample medians and bootstrap 95% confidence intervals.4 Table 5 shows the difference in sample medians, its bootstrap 95% confidence interval and p-value.5 Although the confidence intervals of the individual medians in Table 4 overlap slightly, Table 5 indicates that the weight distributions of Groups 4A and 4B differ significantly at the 5% significance level. However, due to the small number of observations, this segmentation of third staters cannot be considered completely certain and the only possible one.

	median	95% confidence interval
Group 4A	3.56	3.51	3.59
Group 4B	3.49	3.47	3.52

Table 4: Medians and their confidence intervals

	difference in medians	95% confidence interval		p-value
Group 4A vs Group 4B	0.07	0.01	0.11	0.015

Table 5: Differences in medians