Chapter 13, Problem 82H

King Manuel I, Komnenus ruled the Byzantine Empire from Constantinople (Istanbul) during the years 1145 to 1180

A.D. The empire was very powerful during his reign, but declined significantly afterwards. Coins minted during his era

were found in Cyprus, an island in the eastern Mediterranean Sea. Nine coins were from his first coinage, seven from the

second, four from the third, and seven from a fourth. These spanned most of his reign. We have data on the silver content

of the coins:

First Coinage	Second Coinage	Third Coinage	Fourth Coinage
5.59	6.9	4.9	5.3
6.8	9	5.5	5.6
6.4	6.6	4.6	5.5
7	8.1	4.5	5.1
6.6	9.3		6.2
7.7	9.2		5.8
6.9	8.6		5.8
6.2

Table 13.36

Did the silver content of the coins change over the course of Manuel’s reign?

Here are the means and variances of each coinage. The data are unbalanced.

	First	Second	Third	Fourth
Mean	6.7444	8.2429	4.875	5.6143
Variance	0.2953	1.2095	0.2025	0.1314

Table 13.37