Summary Analysed coins Obols Lower silver denominations

Summary

The data suggest that obols can be divided into three groups based on their weight: Types 5.10–11 (Group 5A), Types 5.1–9 and 5.13 (Group 5B), and Type 5.12 (Group 5C). These groups probably correspond to the relative chronology of obol coinage. The decreases in the weight standard between these groups, expressed as differences in the average observed weights, are 0.18 g and 0.17 g, representing decreases of 20.5% and 24.3%, respectively. The differences between the observed medians are 0.17 g and 0.16 g, representing decreases of 19.5% and 22.9%, respectively.

It seems that hemiobols and tetartemorions were minted before the second lowering of the weight standard for obols, i.e. before the minting of obols of Type 5.12. However, the corpus of lower denominations contains very little data so far, and any conclusions are therefore highly speculative.

Analysed coins

Coin catalogue section:	Nagidos, Silver fractions
Coin corpus datasets:	Nagidos, Silver fractions

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 2 November 2025
	Total	Excluded	Analysed
Nagidos, Silver fractions, obols	233	1	232
Nagidos, Silver fractions, hemiobols	3	1	2
Nagidos, Silver fractions, tetartemorions	1		1

Table 1: Numbers of analysed coins

Obols

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
5.1	27	0.76	0.75	0.08	0.11
5.2	8	0.69	0.68	0.12	0.13
5.3	7	0.72	0.72	0.04	0.04
5.4	3	0.62	0.60	0.07	0.10
5.5	13	0.73	0.74	0.04	0.05
5.6	60	0.67	0.69	0.07	0.09
5.7	1	0.68	0.68
5.8	37	0.69	0.68	0.07	0.09
5.9	27	0.70	0.69	0.06	0.06
5.10	12	0.87	0.87	0.07	0.08
5.11	1	0.98	0.98
5.12	19	0.53	0.54	0.05	0.07
5.13	17	0.74	0.74	0.08	0.07

Table 2: Basic descriptive statistics of coin types

As Figure 1 and Table 2 show, the obols can be divided into three groups according to their weight:

Group 5A:	Types 5.10–11;
Group 5B:	Types 5.1–9 and 5.13;
Group 5C:	Type 5.12.

Table 3 shows the descriptive statistics of these groups.

Statistics	Group 5A	Group 5B	Group 5C
Number of coins:	13	200	19
Mean:	0.88	0.70	0.53
Standard deviation:	0.07	0.08	0.05
Interquartile range:	0.08	0.08	0.07
Skewness:	0.61	0.24	0.00
Kurtosis:	2.92	3.73	1.81
Minimum:	0.78	0.51	0.45
25th percentile:	0.83	0.66	0.49
Median:	0.87	0.70	0.54
75th percentile:	0.92	0.74	0.56
Maximum:	1.04	0.95	0.61

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 0.45 to 1.05 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 5A, 5B and 5C

Figure 3: Relative frequency histograms of Groups 5A, 5B and 5C

Figure 4: Cumulative distributions of Groups 5A, 5B and 5C

The distribution of Group 5C is asymmetric. Instead of comparing means, it is therefore statistically more appropriate to compare medians. Since the analysed data have many tied values, the percentile bootstrap method was chosen. Table 4 shows the observed sample medians and bootstrap 95% confidence intervals.3 Table 5 lists all pairwise differences in sample medians, their bootstrap 95% confidence intervals and p-values.4 Since the p-values of all pairwise tests are less than the Bonferroni correction (0.05/3 = 0.0167), we can conclude at the 5% significance level that the weight standards decrease from Group 5A to Group 5B and from Group 5B to Group 5C.

	median	95% confidence interval
Group 5A	0.87	0.84	0.91
Group 5B	0.70	0.69	0.71
Group 5C	0.54	0.49	0.56

Table 4: Medians and their confidence intervals

	difference in medians	95% confidence interval		p-value
Group 5A vs Group 5B	0.17	0.13	0.22	<0.001
Group 5A vs Group 5C	0.33	0.30	0.41	<0.001
Group 5B vs Group 5C	0.16	0.14	0.21	<0.001

Table 5: Differences in medians

Lower silver denominations

The coin corpus on this website so far contains only three hemiobols and one tetartemorion. Moreover, the weight of one of these three hemiobols is not known, and the weight of one of the remaining two hemiobols is known only to one decimal place. Therefore, no statistically based conclusions can be drawn, and we must confine ourselves to preliminary and uncertain observations.

The designs of the hemiobol types known so far (Types 6.1 and 6.2) corresponds to the obols of Types 5.1 and 5.3. The mean and median weights of the obols of these two types are both 0.75 g. Assuming that the weight of hemiobol Ref. No. NA6003 in the coin corpus is 0.40 g (i.e. that the author of the auction catalogue simply rounded the reported value), a preliminary estimate of both the mean and median weight of hemiobols is 0.41 g. This corresponds to approximately 55% of the mean and median weights of obols of Types 5.1 and 5.3, whereas one would expect a value below 50%. The value of 0.41 g is also relatively close to the mean and median of Group 5C, which are 0.53 g and 0.54 g, respectively (see Table 3). Thus, these hemiobols were probably struck earlier than the obols of Group 5C, which were struck at a reduced weight standard.

The weight of the tetartemorion is 0.23 g, which would correspond to an obol weighing 0.92 g. This might suggest that this tetartemorion was struck in the same weight standard as the obols of Group 5A, i.e. obols of Types 5.10 and 5.11. However, no conclusions can be drawn on the basis of a single coin.