Question

5. The quarterly sales data for three consecutive years are listed in the table below Year Quarter Sales MA CMA Index 0S0 1 1690 1938.75 2 940 19662 3 2625 1956.25 1952.5 1.34443 2500 2025 1961.25 1.27469 1800 1990 1990.625 0904239 900 2002.5 2007.5 0.448319 2900 2052.5 1996.25 1.452724 8 | 2360 | 2060 | 20275|1.163995 9 1850 2123.75 2056.25 0.899696 10 I 1100 2091.875 0.525844 11 2930 12 2615 MA refers to Moving Average computed with N 1 CMA refers to the Centered Moving A verage and these are rightfully placed in their respective cells. Index refers to the index for the respective quarter as it appers in the respective row. The respective indices has been computed where ever possible. (4 marks) (2 marks) (a) Compute the quarterly indices; that is: Qi, Q2, Qs and Qi (b) Complete the column labeled SI (Seasonal Indices) (c) Complete the column labeled DSD (DeSeasonalized Data). (I marks)

Answer 1

a) The quarterly index is given below

	Year 1	Year 2	Year 3	Average
Quarter 1		0.904239	0.899696	0.901968
Quarter 2		0.448319	0.525844	0.487082
Quarter 3	1.34443	1.452724		1.398577
Quarter 4	1.274697	1.163995		1.219346

b) and c) is given below in the table

Year		Sales (Yt)	MA(4)	CMA	RTMA= Yt/CMA	SI=S-Index	DSD=Yt/S-Index
Year1	Quarter 1	1690				0.901968	1873.68
	Quarter 2	940				0.487082	1929.86
	Quarter 3	2625	1938.75	1952.50	1.34443	1.398577	1876.91
	Quarter 4	2500	1966.25	1961.25	1.274697	1.219346	2050.28
Year2	Quarter 1	1800	1956.25	1990.63	0.904239	0.901968	1995.64
	Quarter 2	900	2025.00	2007.50	0.448319	0.487082	1847.74
	Quarter 3	2900	1990.00	1996.25	1.452724	1.398577	2073.54
	Quarter 4	2360	2002.50	2027.50	1.163995	1.219346	1935.46
Year3	Quarter 1	1850	2052.50	2056.25	0.899696	0.901968	2051.07
	Quarter 2	1100	2060.00	2091.88	0.525844	0.487082	2258.35
	Quarter 3	2930	2123.75			1.398577	2094.99
	Quarter 4	2615				1.219346	2144.59