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Applied Mathematics · 2026 · 4 marks
CBSE 2026 · Central · Set 4 · Q37
When observed over a long period of time, a time series data can predict trends that can forecast increase or decrease or stagnation of a variable…
When observed over a long period of time, a time series data can predict trends that can forecast increase or decrease or stagnation of a variable under consideration. Such analytical studies can benefit a business for forecasting or prediction of future estimated sales or production.
Mathematically, for finding a line of best-fit to represent a trend, many methods are available. Methods like moving averages and least squares are some of the techniques to predict such trends.
Mr. Nitin runs a soap-making factory and the record of his sales of soaps for the period $\displaystyle 2018$ – $\displaystyle 2024$ is as follows :
| Year | $\displaystyle 2018$ | $\displaystyle 2019$ | $\displaystyle 2020$ | $\displaystyle 2021$ | $\displaystyle 2022$ | $\displaystyle 2023$ | $\displaystyle 2024$ |
| Sales (in ₹ thousands) | $\displaystyle 80$ | $\displaystyle 90$ | $\displaystyle 92$ | $\displaystyle 83$ | $\displaystyle 94$ | $\displaystyle 99$ | $\displaystyle 92$ |
Based on the above information, answer the following questions :
(i)
Obtain the trend line to the given data.
(ii)
Find the average change in the sales.
(iii)
(a)
Find the sum of the differences between the actual sales and the trend values (for $\displaystyle 2018$ – $\displaystyle 2024$).
OR
(b)
What are the expected sales for the year $\displaystyle 2025$?
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