Question

Calculate the mean, variance, standard deviation, coefficient of variation for each country

What can you tell about the variability of the exchange rates of the nine OECD countries?

Calculate co-variance and correlation coefficients for the following two pairs of countries: (1) Japan and UK; (2) China and Korea

What can you tell about the relationship of the exchange rates between Japan and UK?

What can you tell about the relationship of the exchange rates between China and Korea?

TABLE 1.4 Foreign exchange rates, 1985–2006
[Foreign currency units per U.S. dollar, except as noted; certified noon buying rates in New York]
Period	Australia (dollar) 2	Canada (dollar)	China, P.R. (yuan)	Japan (yen)	Mexico (peso)	South Korea (won)	Sweden (krona)	Switzerland (franc)	United Kingdom (pound) 2
1985	0.7003	1.3659	2.9434	238.47	0.257	872.45	8.6032	2.4552	1.2974
1986	0.6709	1.3896	3.4616	168.35	0.612	884.60	7.1273	1.7979	1.4677
1987	0.7014	1.3259	3.7314	144.60	1.378	826.16	6.3469	1.4918	1.6398
1988	0.7841	1.2306	3.7314	128.17	2.273	734.52	6.1370	1.4643	1.7813
1989	0.7919	1.1842	3.7673	138.07	2.461	674.13	6.4559	1.6369	1.6382
1990	0.7807	1.1668	4.7921	145.00	2.813	710.64	5.9231	1.3901	1.7841
1991	0.7787	1.1460	5.3337	134.59	3.018	736.73	6.0521	1.4356	1.7674
1992	0.7352	1.2085	5.5206	126.78	3.095	784.66	5.8258	1.4064	1.7663
1993	0.6799	1.2902	5.7795	111.08	3.116	805.75	7.7956	1.4781	1.5016
1994	0.7316	1.3664	8.6397	102.18	3.385	806.93	7.7161	1.3667	1.5319
1995	0.7407	1.3725	8.3700	93.96	6.447	772.69	7.1406	1.1812	1.5785
1996	0.7828	1.3638	8.3389	108.78	7.600	805.00	6.7082	1.2361	1.5607
1997	0.7437	1.3849	8.3193	121.06	7.918	953.19	7.6446	1.4514	1.6376
1998	0.6291	1.4836	8.3008	130.99	9.152	1,400.40	7.9522	1.4506	1.6573
1999	0.6454	1.4858	8.2783	113.73	9.553	1,189.84	8.2740	1.5045	1.6172
2000	0.5815	1.4855	8.2784	107.80	9.459	1,130.90	9.1735	1.6904	1.5156
2001	0.5169	1.5487	8.2770	121.57	9.337	1,292.02	10.3425	1.6891	1.4396
2002	0.5437	1.5704	8.2771	125.22	9.663	1,250.31	9.7233	1.5567	1.5025
2003	0.6524	1.4008	8.2772	115.94	10.793	1,192.08	8.0787	1.3450	1.6347
2004	0.7365	1.3017	8.2768	108.15	11.290	1,145.24	7.3480	1.2428	1.8330
2005	0.7627	1.2115	8.1936	110.11	10.894	1,023.75	7.4710	1.2459	1.8204
2006	0.7535	1.1340	7.9723	116.31	10.906	954.32	7.3718	1.2532	1.8434

Answer 1

	Mean	Variance	SD	CoV
Australia	0.701982	0.00602	0.077591	0.110531
Canada	1.33715	0.016133	0.127017	0.094991
China	6.675473	4.170869	2.042271	0.305936
Japan	127.7686	851.6631	29.18327	0.228407
Mexico	6.155455	14.3816	3.792308	0.616089
South Korea	952.105	44290.12	210.4522	0.221039
Sweden	7.509609	1.405948	1.185727	0.157895
Switzerland	1.489541	0.069502	0.263632	0.176989
United Kingdom	1.628009	0.020195	0.142108	0.08729

Among nine OECD countries by seeing the cofficient of variation one can see that minimum and maximum variability is seen in United kingdom and Maxico which is approximately 8.7% and 66.6% respectively.

(b) Co-variance and correlation coefficients for the Japan and UK is -1.72 and -0.414 and for countries China and Korea is 263.3511 and 0.613 respectively. we can see that the correlation coefficient is negative for Japan and UK that shows the behaviour of Foreign exchange rates data is different for both countries (it means if one is increasing than other is decreasing). and for countries China and Koria the correlation coefficient is positive that shows same behaviour of data for both countries.