Basic statistics Comparison with Kelenderis staters

Coin catalogue section: |
Pseudo-Kelenderis Mints |

Coin corpus dataset: |
Pseudo-Kelenderis Mints |

### Basic statistics

Box plots1 are presented in Figure 1, with the single specimens of Types 1a and 2 represented by red horizontal lines. Descriptive statistics of Type 1 are shown in Table1. A total of 16 specimens of Type 1 are analyzed, as the weight of coins nos. 17–18 (Vismara 1999 and Münzhandel A. J. Koci) are not known. Coin no. 2 (Numismatik Naumann, Auction 55, Lot 359) is distinguished from other coins by its very low weight of 9.84 g. According to the photograph in the auction catalogue, it appears to be well preserved and without signs of metal degradation.

**Figure 1: **Box plots

Statistics | Type 1 |
---|---|

Number of coins: |
16 |

Mean: |
10.61 |

Standard deviation: |
0.29 |

Interquartile range: |
0.33 |

Skewness: |
-1.29 |

Kurtosis: |
4.10 |

Minimum: |
9.84 |

25th percentile: |
10.47 |

Median: |
10.70 |

75th percentile: |
10.80 |

Maximum: |
10.93 |

**Table 1:** Descriptive statistics of Type 1

Figure 2 presents the relative frequency histogram. The bars represent the relative frequencies of Type 1 coins ranging from 9.80 to 11.00 g in increments of 0.10 g. The isolated bar on the left corresponds to the outlier mentioned above (coin no. 2). Weights of the only known specimen of Type 2 is represented by the blue circle on the horizontal axis.

**Figure 2: **Relative frequency histogram

### Comparison with Kelenderis staters

Kelenderis staters are divided into Groups 1, 2 and 3 (see page Coin Catalogue / Kelenderis / Overview), with Group 3 being divided into the following into the following three subgroups (see page Weight Analyses / Kelenderis, staters):

Group 3A: |
Types 3.1–3 and 3.7–12, i.e. coins of Group 3 except Types 3.4–6 and 3.13–17; |

Group 3B: |
Types 3.13–14; |

Group 3C: |
Types 3.4–6 and 3.15–17. |

A comparison of both types of Pseudo-Kelenderis staters with individual groups of Kelenderis staters is shown in Figure 3. These box plots suggest that the weight distribution of Pseudo-Kelenderis Type 1 coins best corresponds to the Kelenderis Group 3A.2 It is therefore possible that the minting of these coins can be dated to approximately the same time period. Relative frequency histograms and cumulative distributions of Pseudo-Kelenderis Type 1 and Kelenderis Group 3A are presented in Figures 4 and 5, respectively. As for Pseudo-Kelenderis Type 2, no conclusions can be drawn on the basis of a single specimen.

**Figure 3: **Kelenderis vs Pseudo-Kelenderis staters, box plots

**Figure 4: **Kelenderis vs Pseudo-Kelenderis staters, relative frequency histograms

**Figure 5: **Kelenderis vs Pseudo-Kelenderis staters, cumulative distributions

1The bottom and top of each box are the 25th and 75th percentiles of the dataset, respectively (the lower and upper quartiles). Thus, the height of the box corresponds to the interquartile range (IQR). The red line inside the box indicates the median. Whiskers (the dashed lines extending above and below the box) indicate variability outside the upper and lower quartiles. From above the upper quartile, a distance of 1.5 times the IQR is measured out and a whisker is drawn up to the largest observed data point from the dataset that falls within this distance. Similarly, a distance of 1.5 times the IQR is measured out below the lower quartile and a whisker is drawn down to the lowest observed data point from the dataset that falls within this distance. Observations beyond the whisker length are marked as outliers and are represented by small red circles.

2The Kolmogorov–Smirnov statistics of Pseudo-Kelenderis Type 1 versus Kelenderis Groups 1, 2, 3A, 3B and 3C are 0.313, 0.291, 0.159, 0.344 and 0.938, respectively. P-value of Kolmogorov-Smirnov test of the equality of weight distribution of Pseudo-Kelenderis Type 1 and the Kelenderis Group 3A is 0.822 (the equality of distributions is not rejected at the 5% level of significance).

2 April 2022 – 30 December 2023