What is a moving averages and how is it calculated?

Simple moving average explanation with chart examples and formula

Daily Temperature	16	19	21	20	24	21	16	17	11	14	13	20	21

3 Day Moving Average	-	-	18.6	20.0	21.6	21.6	20.3	18.0	14.6	14.0	12.6	15.6	18.0

In the table above you can see the daily temperature and below is the "simple moving average" of the daily temperature.

The colour coding is used to show how the calculations are made. The first three days are 16, 19, 21 which produce an 3 day average of 18.67.

The calculation is very simple.

Day 1 (16) + Day 2 (19) + Day 3 (21) = 56 then we simply divide 56 by 3 days ( as we are making a three day moving average )

The correct mathematic statement for this would be (16+19+21) / 3

The next stage in creating a true moving average is to roll forward to the right by 1 number. So for the next value we will use Days 2 ,3 and 4

Therefore (19+21+20) / 3 = 20 this procedure repeats each time a new value or a new day is added to the array of temperatures. You can see of course that 3 days are required to produce the three day average. Another important factor to understand is that this action of waiting for three days before calculating a value produces a delay in the average which is outputted. This delay is know as LAG.

If you look at the Last temperature of 21 you will realise that the 3 day average of 18 is actually "LAGGING BEHIND"

The chart below is a graphic illustration of the daily temperature and the three day average of it.

3 period moving average

Key points to remember

Moving averages produce a smoother output value than the actual data value
Moving averages produce a delay know as lag.
Moving averages need 3 days to compute the first value ( if a three day average is required )
Moving averages reduce fluctuation and smooth out "noise" ( Noise is a term used for jagged and messy data fluctuations )

6 Day moving average calculation example

Stock market price	41	42	40	38	39	36	36	33	32	28	29	33	36	39	44

6 Day Moving Average	-	-	-	-	-	39.33	38.50	37.00	35.67	34.00	32.33	31.83	31.83	32.83	34.83

In the table above you can see the daily stock market price and below is the "six day simple moving average" of that stock price.

The colour coding is used to show how the calculations are made. The first six days are coloured orange 41,42,40,38,39,36 which produce an 6 day average of 39.33

The calculation is very simple and follows the same method as the first example. However this time the first 6 days are added together and divided by 6 because this time it a 6 day average instead of 3 days as was used in the first example.

Day 1 (41) + Day 2 (42) + Day 3 (40) + Day 4 (38) + Day 5 (39) + Day 6 (36) = 236 then we simply divide 236 by the 6 days ( as we are making a six day moving average )

The correct mathematic statement for this would be (41+42+40+38+39+36) / 6

The next stage in creating a true moving average is to roll forward to the right by 1 number. So for the next value we will use Days 2, 3, 4, 5, 6, 7

The chart below is a graphic illustration of the daily stock price and six day average of it.

six period SMA

The 6 day moving average is clearly making a smoother indication of the stock price.
Note the delay (LAG) in the response time of the yellow average line. It turns up on 3 days later than the stock price
Moving averages can be used to smooth erratic data so as to be clearer to understand and interpret.
Note how the 6 day moving average is smoother than the 3 day moving average.
The more days ( periods ) used in the calculation the smoother they will become, and the more lag they will have.

Mathematical symbol for AVERAGE

Maths symbol for average (sma)

Other types of moving average and formulas

Simple moving average
Weighted moving average
Exponential moving average
Triangular moving average
Hull moving average

A very advanced type of moving average is shown below. PLA Dynamical has over 1000 lines of computer code used to generate its output