# Obtain trend values for the following data using 4-yearly centered moving averages. Year 1971 1972 1973 1974 1975 1976 Production 1 0 1 2 3 2 Year 1977 1978 1979 1980 1981 1982 Production 3 6 5 1 4 10 - Mathematics and Statistics

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Obtain trend values for the following data using 4-yearly centered moving averages.

 Year 1971 1972 1973 1974 1975 1976 Production 1 0 1 2 3 2 Year 1977 1978 1979 1980 1981 1982 Production 3 6 5 1 4 10

#### Solution

Construct the following table for obtaining 4-yearly centered moving average for the data:

 Year t Production yt 4–yearly moving total 4–yearly moving average 2 unit moving total 4–yearly centred moving averages trend value 1971 1 1972 0 4 1 1973 1 6 1.5 2.5 1.25 1974 2 8 2 3.5 1.75 1975 3 10 2.5 4.5 2.25 1976 2 14 3.5 6 3 1977 3 16 4 7.5 3.75 1978 6 15 3.75 7.75 3.875 1979 5 16 4 7.75 3.875 1980 1 20 5 9 4.5 1981 4 - - - - 1982 10 - - - -
Concept: Measurement of Secular Trend
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Chapter 4: Time Series - Miscellaneous Exercise 4 [Page 69]

#### APPEARS IN

Balbharati Mathematics and Statistics 2 (Commerce) 12th Standard HSC Maharashtra State Board
Chapter 4 Time Series
Miscellaneous Exercise 4 | Q 4.06 | Page 69
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