# How to Calculate the 3 Point Moving Averages From a List of Numbers and Describe the Trend

*Mark, a math enthusiast, loves writing tutorials for stumped students and those who need to brush up on their math skills.*

To calculate the 3 point moving averages form a list of numbers, follow these steps:

1. Add up the first 3 numbers in the list and divide your answer by 3. Write this answer down as this is your first 3 point moving average.

2. Add up the next 3 numbers in the list and divide your answer by 3. Write this answer down as this is your second 3 point moving average.

3. Keep repeating step 2 until you reach the last 3 numbers.

Make sure you press the equals key when you’ve added the numbers up or you will only divide the last number by 3 (or insert brackets around the sum as shown in the examples below).

Finding the moving averages will help you identify the trend as you will see in the next 2 examples.

**Example 1**

The temperatures measured in London for the first week in July were as follows:

21⁰C, 24⁰C, 21⁰C, 27⁰C, 30⁰C, 28.5⁰C and 36⁰C

Calculate all of the 3 point moving averages and describe the trend.

1^{st} 3 point moving average:

(21 + 24 + 21) ÷ 3 = 22⁰C

The 2^{nd} 3 point moving average is:

(24 + 21 + 27) ÷ 3 = 24⁰C

The 3^{rd} 3 point moving average is:

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(21 + 27 + 30) ÷ 3 = 26⁰C

The 4^{th} 3 point moving average is:

(27 + 30 + 28.5) ÷ 3 = 28.5⁰C

The 5^{th} 3 point moving average is:

(30 + 28.5 + 36) ÷ 3 = 31.5⁰C

So the 3 point moving averages are:

22, 24, 26, 28.5 and 31.5

Since these moving averages are increasing then the general trend is that the temperatures are rising through the week.

**Example 2**

A shop records it’s sales figures for the first 6 months of the year:

January = £936

February = £939

March = £903

April = £870

May = £882

June = £810

Calculate all of the 3 point moving averages and describe the trend:

1^{st} 3 point moving average:

(936 + 939 + 903) ÷ 3 = £926

The 2^{nd} 3 point moving average is:

(939 + 903 + 870) ÷ 3 = £904

The 3^{rd} 3 point moving average is:

(903 + 870 + 882) ÷ 3 = £885

The 4^{th} 3 point moving average is:

(870 + 882 + 810) ÷ 3 = £854

So the 3 point moving averages are £926, £904, £885 and £854. Since the moving averages are decreasing then the sales figures are going down as the months go by.

## Questions & Answers

**Question:** On a graph, would the first moving average be plotted half way through the Feb column?

**Answer:** Plot the point half-way between the 3 numbers you were dividing. So if it was for January, February and March plot the point on February.

**Question:** How do you perform a 6 point moving average?

**Answer:** Add up the first 6 numbers and divide by 6.

Then add up the next 6 numbers and divide by 6.

Keep repeating.