Find the trend using four yearly moving averages for the following data showing yearly sales (in lakh ₹) of a shop : | Year | 2015 | 2016 | 2017 | 2018 | 2019 | 2020 | 2021 | 2022 | 2023 | 2024 | |---|---|---|---|---|---|---|---|---|---|---| | Sales (lakh ₹) | 5 | 3 | 7 | 6 | 4 | 8 | 9 | 10 | 8 | 9 |

Find the trend using four yearly moving averages for the following data showing yearly sales (in lakh ₹) of a

Question 34 of 41

Find the trend using four yearly moving averages for the following data showing yearly sales (in lakh ₹) of a shop :

Year	2015	2016	2017	2018	2019	2020	2021	2022	2023	2024
Sales (lakh ₹)	5	3	7	6	4	8	9	10	8	9

Gujarat GsebGujarat Board (GSEB) HSC Commerce Board 2025Subjective· 5mImportance★★★★★

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4-yearly moving averages are centred (2-item average) to give the trend: 2017 → 5.125, 2018 → 5.625, 2019 → 6.5, 2020 → 7.25, 2021 → 8.25, 2022 → 8.875.

GSEB Class-12 Statistics, Time Series (moving average method, even period):

For a 4-yearly moving average the period is even, so the moving averages fall between years and must be centred by taking a further 2-item moving average.

Step 1 — 4-yearly moving totals and averages:

Year	Sales	4-yearly moving total	4-yearly moving average
2015	5
2016	3
		$5+3+7+6 = 21$	$21/4 = 5.25$
2017	7
		$3+7+6+4 = 20$	$20/4 = 5.00$
2018	6
		$7+6+4+8 = 25$	$25/4 = 6.25$
2019	4
		$6+4+8+9 = 27$	$27/4 = 6.75$
2020	8
		$4+8+9+10 = 31$	$31/4 = 7.75$
2021	9
		$8+9+10+8 = 35$	$35/4 = 8.75$
2022	10
		$9+10+8+9 = 36$	$36/4 = 9.00$
2023	8
2024	9
…

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