Calculate four-yearly moving averages of number of students studying in a higher secondary school in a particular city from the following data. | Year | 2001 | 2002 | 2003 | 2004 | 2005 | 2006 | 2007 | 2008 | 2009 | | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | | Number of students | 124 | 120 | 135 | 140 | 145 | 158 | 162 | 170 | 175 |

> > [!TLDR] > Form 4-year moving totals, average them, then centre (average adjacent pairs) to get trend values for 2003–2007, all rising. > > **Step 1 — 4-year moving totals and averages** (placed at the mid-point of each block of four): > > | Years | Total | 4-yr average | Centred at | > | --- | --- | --- | --- | > | 2001–2004 | $124{+}120{+}135{+}140 = 519$ | $129.75$ | 2002.5 | > | 2002–2005 | $120{+}135{+}140{+}145 = 540$ | $135.00$ | 2003.5 | > | 2003–2006 | $135{+}140{+}145{+}158 = 578$ | $144.50$ | 2004.5 | > | 2004–2007 | $140{+}145{+}158{+}162 = 605$ | $151.25$ | 2005.5 | > | 2005–2008 | $145{+}158{+}162{+}170 = 635$ | $158.75$ | 2006.5 | > | 2006–2009 | $158{+}162{+}170{+}175 = 665$ | $166.25$ | 2007.5 | > > **Step 2 — centre the averages** (average each adjacent pair so the value lines up with a year): > > | Year | Centred 4-yearly moving average | > | --- | --- | …

Calculate four-yearly moving averages of number of students studying in a higher secondary school in a particu

Question 17 of 39

Calculate four-yearly moving averages of number of students studying in a higher secondary school in a particular city from the following data.

Year	2001	2002	2003	2004	2005	2006	2007	2008	2009
Number of students	124	120	135	140	145	158	162	170	175

Tamil Nadu DgeTamil Nadu HSC (DGE) Commerce Board 2020Subjective· 3mImportance★★★★★

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Form 4-year moving totals, average them, then centre (average adjacent pairs) to get trend values for 2003–2007, all rising.

Step 1 — 4-year moving totals and averages (placed at the mid-point of each block of four):

Years	Total	4-yr average	Centred at
2001–2004	$124{+}120{+}135{+}140 = 519$	$129.75$	2002.5
2002–2005	$120{+}135{+}140{+}145 = 540$	$135.00$	2003.5
2003–2006	$135{+}140{+}145{+}158 = 578$	$144.50$	2004.5
2004–2007	$140{+}145{+}158{+}162 = 605$	$151.25$	2005.5
2005–2008	$145{+}158{+}162{+}170 = 635$	$158.75$	2006.5
2006–2009	$158{+}162{+}170{+}175 = 665$	$166.25$	2007.5

Step 2 — centre the averages (average each adjacent pair so the value lines up with a year):

| Year | Centred 4-yearly moving average |

| --- | --- | …

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