Find the trend using four monthly moving averages for the following data showing monthly sales (in lakhs ₹) of a shop. | Month | Sales (lakh ₹) | |---|---| | March | 5 | | April | 3 | | May | 7 | | June | 6 | | July | 4 | | August | 8 | | September | 9 | | October | 10 | | November | 8 | | December | 9 |

> > [!TLDR] > 4-month totals: 21,20,25,27,31,35,36; centred trend $=\dfrac{\text{two consecutive totals}}{8}$ → May 5.125, Jun 5.625, Jul 6.5, Aug 7.25, Sep 8.25, Oct 8.875. > > **Data (monthly sales, lakh ₹):** Mar 5, Apr 3, May 7, Jun 6, Jul 4, Aug 8, Sep 9, Oct 10, Nov 8, Dec 9. > > **Step 1 — 4-monthly moving totals.** > > | Months | 4-month total | > |---|---| > | Mar–Jun | 5+3+7+6 = 21 | > | Apr–Jul | 3+7+6+4 = 20 | > | May–Aug | 7+6+4+8 = 25 | > | Jun–Sep | 6+4+8+9 = 27 | > | Jul–Oct | 4+8+9+10 = 31 | > | Aug–Nov | 8+9+10+8 = 35 | > | Sep–Dec | 9+10+8+9 = 36 | > > **Step 2 — centre the totals** (average of two consecutive 4-month totals, divided by 4 — equivalently sum $\div 8$), which aligns the trend with an actual month. > > | Month | Centred trend $=\dfrac{\text{sum of two consecutive totals}}{8}$ | > |---|---| > | May | $(21+20)/8 = 41/8 = 5.125$ | > | June | $(20+25)/8 = 45/8 = 5.625$ | …

Find the trend using four monthly moving averages for the following data showing monthly sales (in lakhs ₹) of

Question 22 of 41

Find the trend using four monthly moving averages for the following data showing monthly sales (in lakhs ₹) of a shop.

Month	Sales (lakh ₹)
March	5
April	3
May	7
June	6
July	4
August	8
September	9
October	10
November	8
December	9

Gujarat GsebGujarat Board (GSEB) HSC Commerce Board 2022Subjective· 5mImportance★★★★★

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4-month totals: 21,20,25,27,31,35,36; centred trend $=\dfrac{\text{two consecutive totals}}{8}$ → May 5.125, Jun 5.625, Jul 6.5, Aug 7.25, Sep 8.25, Oct 8.875.

Data (monthly sales, lakh ₹): Mar 5, Apr 3, May 7, Jun 6, Jul 4, Aug 8, Sep 9, Oct 10, Nov 8, Dec 9.

Step 1 — 4-monthly moving totals.

Months	4-month total
Mar–Jun	5+3+7+6 = 21
Apr–Jul	3+7+6+4 = 20
May–Aug	7+6+4+8 = 25
Jun–Sep	6+4+8+9 = 27
Jul–Oct	4+8+9+10 = 31
Aug–Nov	8+9+10+8 = 35
Sep–Dec	9+10+8+9 = 36

Step 2 — centre the totals (average of two consecutive 4-month totals, divided by 4 — equivalently sum $\div 8$ ), which aligns the trend with an actual month.

Month	Centred trend $=\dfrac{\text{sum of two consecutive totals}}{8}$
May	$(21+20)/8 = 41/8 = 5.125$
June	$(20+25)/8 = 45/8 = 5.625$

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