# How to calculate a 4 point moving average in your math or statistics exam.

A 4 point average can be used to identify a trend within a data set over a period of time. In order to calculate the 4 point moving averages from a list of data follow these simple steps:

Step 1 Find the total of the first 4 numbers and divide by 4.

Step 2 Find the total of the next 4 numbers and divide by 4.

Step 3 Repeat Step 2, until no more 4 point averages can be taken.

Let’s take a look at a couple of examples:

**Example**

Billy is selling DVD’s on the internet. Here are his sales for the first 6 months of the year. Work out the 4 point moving averages for this data and describe the trend.

January = 18

February = 16

March = 21

April = 23

May = 21

June = 26

Step 1 Find the total of the first 4 numbers and divide by 4.

1^{st} 4 point average = (18+16+21+23)/4 = 17

Step 2 Find the total of the next 4 numbers and divide by 4.

2^{nd} 4 point average = (16 + 21 + 23+ 21)/4 = 20.25

Step 3 Repeat step 2 until no more 4 point averages can be taken.

3^{rd} 4 point moving average = (21+23+21+26) = 22.75

You cannot calculate anymore 4 point moving averages as there are no figures for July.

So the 4 point moving averages so far are 17, 20.25 and 22.75. Since this sequence is increasing then the amount of sales is increasing over a period of time. As you can this makes the trend much easier to spot as the DVD’s took a dip in February and May if you just look at the original data.

**Example 2**

Emma wants to know if her wages are on the up or drop. Here are her wages for the first 8 months of the year. Use 4 point averages to identify the trend.

January = 1.4k

February = 1.3k

March = 1.45k

April = 1.1k

May = 1k

June = 1.25k

July 1.05k

August= 1.01k

1^{st} 4 point average = (1.4 + 1.3 + 1.45 + 1.1)/4 = 1.3125

2^{nd} 4 point average = (1.3 + 1.45 + 1.1 + 1)/4 = 1.2125

3^{rd} 4 point average = (1.45 + 1.1 + 1 + 1.25)/4 = 1.2

4^{th} 4 point average = (1.1 + 1 + 1.25 + 1.05)/4 = 1.1

5^{th} 4 point average = (1 + 1.25 + 1.05 + 1.01)/4 = 1.0775

So as you can see the 4 point averages decrease each time so her wages are on the drop. Again, this was much harder to see from the original data as there were increases in March and June.

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