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Question
Write a brief note on seasonal variations
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Solution
Seasonal Variations: As the name suggests, tendency movements are due to nature which repeat themselves periodically in every seasons.
These variations repeat themselves in less than one year time.
It is measured in an interval of time.
Seasonal variations may be influenced by natural force, social customs and traditions.
These variations are the results of such factors which uniformly and regularly rise and fall in the magnitude.
For example, selling of umbrellas’ and raincoat in the rainy season, sales of cool drinks in summer season, crackers in deepawali season, purchase of dresses in a festival season, sugarcane in Pongal season.
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RELATED QUESTIONS
The following table gives the number of small-scale units registered with the Directorate of Industries between 1985 and 1991. Show the growth on a trend line by the free hand method.
| Year | No. of units (in '000) |
| 195 | 10 |
| 986 | 22 |
| 1987 | 36 |
| 198 | 62 |
| 1989 | 55 |
| 1990 | 0 |
| 1991 | 34 |
| 1992 | 50 |
Determine the equation of a straight line which best fits the following data
| Year | 2000 | 2001 | 2002 | 2003 | 2004 |
| Sales (₹ '000) | 35 | 36 | 79 | 80 | 40 |
Compute the trend values for all years from 2000 to 2004
The sales of a commodity in tones varied from January 2010 to December 2010 as follows:
| In Year 2010 | Sales (in tones) |
| Jan | 280 |
| Feb | 240 |
| Mar | 270 |
| Apr | 300 |
| May | 280 |
| Jun | 290 |
| Jul | 210 |
| Aug | 200 |
| Sep | 230 |
| Oct | 200 |
| Nov | 230 |
| Dec | 210 |
Fit a trend line by the method of semi-average
Use the method of monthly averages to find the monthly indices for the following data of production of a commodity for the years 2002, 2003 and 2004
| 2002 | 2003 | 2004 |
| 15 | 20 | 18 |
| 18 | 18 | 25 |
| 17 | 16 | 21 |
| 19 | 13 | 11 |
| 16 | 12 | 14 |
| 20 | 15 | 16 |
| 21 | 22 | 19 |
| 18 | 16 | 20 |
| 17 | 18 | 1 |
| 15 | 20 | 16 |
| 14 | 17 | 18 |
| 18 | 15 | 20 |
Calculate the seasonal indices from the following data using the average method:
| Year | I Quarter | II Quarter | III Quarter | IV Quarter |
| 2008 | 72 | 68 | 62 | 76 |
| 2009 | 78 | 74 | 78 | 72 |
| 2010 | 74 | 70 | 72 | 76 |
| 2011 | 76 | 74 | 74 | 72 |
| 2012 | 72 | 72 | 76 | 68 |
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The components of a time series which is attached to short term fluctuation is
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Factors responsible for seasonal variations are
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Least square method of fitting a trend is
Using three yearly moving averages, Determine the trend values from the following data.
| Year | Profit | Year | Profit |
| 2001 | 142 | 2007 | 241 |
| 2002 | 148 | 2008 | 263 |
| 2003 | 154 | 2009 | 280 |
| 2004 | 146 | 2010 | 302 |
| 2005 | 157 | 2011 | 326 |
| 2006 | 202 | 2012 | 353 |
Sum of the first n terms of the series `1/2 + 3/4 + 7/8 + 15/16 +`......... is equal to:
