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sums will set you free

calculating moving averages

by abelard

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calculating moving averages

One way of dealing with the problems where trends are uncertain is to do what is called a moving average.

  • What you do is to take, say 5, 10, or 12 steps in a time series. Such a series might be
time 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
value 15 33 44 87 67 72 59 36 21 19 13 27 39 52 63 74 51 49

and the selected steps are the ten from 1 to 10.

  • Next action is to average the chosen values:

    (15+33+44+87+67+72+59+36+21+19) / 10 = 45.3

  • Now subtract the first data point:

    and add in the next data point in the series:

    or (33+44+87+67+72+59+36+21+19+13).

  • Average these values (33+44+87+67+72+59+36+21+19+13) / 10 = 45.1

The resulting values, 45.3, 45.1, and so on, form the data points on the moving average graph.

Repeat these actions, as required, to create a ‘moving average’ graph/chart.

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A moving average graph is used to iron out errors/variations. It is particularly useful where there is a regular variation. For instance, where seasons effect the data during over each twelve month period, as with monthly sales in a shop.

In summary, there are various ways and reasons to smooth out data:

  • in cases of regular variation
  • with data subject to ‘random’ perturbation, such as years of temperature data
  • to average out values estimated by different workers.

sums will set you free is included in the series of documents about economics and money at
moneybookers information e-gold information fiat money and inflation
calculating moving averages the arithmetic of fractional banking


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