Moving average: when takings jump at weekends, how can you tell whether sales are really growing or not?

Sunday 7.7 million, Monday 4.1 million: takings "collapsed" by 47 percent in one day. In fact nothing collapsed, it is the ordinary weekly rhythm. A seven-day moving average removes this noise and shows that over three weeks average daily takings grew from 5.33 to 6.01 million soum. How to choose the window length and which mistakes to avoid.

Nodira, the manager of the "Lola" family cafe, writes down yesterday's takings on her phone every morning. On Monday she gets worried: Sunday was 7.7 million soum, Monday only 4.1 million. Almost half in one day. But last Monday was the same.

Key rules

A moving (rolling) average is, for each day, the average of the last few days. Each time a new day is added, the oldest day drops out, and the "window" moves one step forward
The purpose: to smooth out random and periodic fluctuations and show the underlying direction (trend)
The window length should equal the repeating cycle. In a cafe, shop or barbershop the rhythm is weekly, so a 7-day window is taken: each average then contains one of every day from Monday to Sunday
If the window is shorter than the cycle (for example, 3 days), the average also jumps at weekends and smooths out nothing
An average calculated over the last days (backward-looking) shows a real change with a delay: with a 7-day window a turn in the trend is noticed only after several days
An unusual day (a holiday or a day with a one-off large order) keeps the average raised for 7 days: mark such days separately
A moving average is not a forecast, it makes past data understandable. To draw conclusions about the future, compare it with the same period last year

Example: three weeks of daily takings

Takings in million soum, hypothetical, compiled by the author. The 7-day average is calculated from day 7 onwards.

Day	Weekday	Takings	7-day average
1	Mon	4.0
2	Tue	3.6
3	Wed	3.8
4	Thu	4.2
5	Fri	5.6
6	Sat	8.4
7	Sun	7.7	5.33
8	Mon	4.1	5.34
9	Tue	3.9	5.39
10	Wed	4.0	5.41
11	Thu	4.4	5.44
12	Fri	5.9	5.49
13	Sat	8.9	5.56
14	Sun	8.1	5.61
15	Mon	4.5	5.67
16	Tue	4.2	5.71
17	Wed	4.4	5.77
18	Thu	4.7	5.81
19	Fri	6.3	5.87
20	Sat	9.4	5.94
21	Sun	8.6	6.01

Sample calculation, day 8: (3.6 + 3.8 + 4.2 + 5.6 + 8.4 + 7.7 + 4.1) : 7 = 37.4 : 7 ≈ 5.34.

What can be seen: - daily takings jump from 3.6 to 9.4, while the 7-day average grows slowly but steadily every day: from 5.33 to 6.01; - weekly total takings are 37.3 → 39.3 → 42.1 million soum, that is, growth of about 12.9% over three weeks. The Monday "collapse" is just the weekly rhythm; - for comparison, a 3-day window: 7.23 on day 7, 4.00 on day 10. It too jumps with the weekends and does not show the trend.

The conclusion for Nodira: a day should be compared not with the previous day but with the same day last week and with the 7-day average. Monday on day 15 (4.5) is higher than the previous Monday (4.1): sales are growing.

Test yourself

5 questions on this topic: pick an option or reveal the answer.

A tea shop calculated the linear correlation coefficient between advertising spending and weekly sales: r = 0.9. What share of the variation in sales does the coefficient of determination (r²) explain as linked to advertising?

A shop's monthly sales for January–June (mln soum): 10, 12, 17, 14, 13, 18. What is the three-month moving average for April–June?

For the monthly revenue of a bakery's branches, the mean is 50 mln soums and the standard deviation is 10 mln soums. What is the coefficient of variation?

A cafe's takings over 5 days were 2, 3, 4, 5 and 6 mln soum. What are the average daily takings (arithmetic mean)?

A bakery's revenue grew from 100 mln soums to 144 mln soums over two years. What is the average annual growth rate (by the geometric mean method)?

Answered: 0 / 50 of 5 correct

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