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Question 25 of 25
Q.

Following data shows the number of boxes of cereal sold in years 1977 to 1984.

Year19771978197919801981198219831984
No. of boxes in ten thousand103810458
Fit a trend line to the above data by graphical method.
Maharashtra MsbshseMaharashtra HSC (MSBSHSE) Board 2026Subjective· 3mImportance★★★★★
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Plot (year, boxes) and draw one smooth freehand line balancing the points above and below it; the fitted line rises from about 1–2 (ten-thousands) near 1977 to about 7–8 near 1984, i.e. an increasing trend.

Data (boxes sold, in ten-thousands):

Year19771978197919801981198219831984
Boxes103810458

Graphical (freehand) method — procedure:

  1. Take years on the X-axis and the number of boxes (ten-thousands) on the Y-axis, choosing a suitable scale (e.g. 1 unit = 1 year on X, 1 unit = 1 ten-thousand on Y).
  2. Plot the eight points (1977,1)(1977,1), (1978,0)(1978,0), (1979,3)(1979,3), (1980,8)(1980,8), (1981,10)(1981,10), (1982,4)(1982,4), (1983,5)(1983,5), (1984,8)(1984,8) and join them to see the actual (fluctuating) series.
  3. Draw a single smooth freehand straight/curved line through the scatter so that it moves evenly among the points — roughly as many points lie above the line as below it, and the line ignores the short-term ups and downs. …

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