# How to calculate running average

Written by kelvin o'donahue
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A running average can be either of two measurements. A cumulative running average includes all values, and is updated whenever a new value is added to the data set. Running average may also refer to moving average, or the average of a subset of the most recent measurements.

You might calculate the cumulative running average of the age of everyone in a club. Every time a new member joins, the cumulative average changes. A moving average could be the average high temperature over the last two weeks: each day, the set of data used to calculate the average “moves” one day.

Skill level:
Easy

### Things you need

• Calculator (optional)

## Instructions

1. 1

Sum all data values. For example, the sum of the seven numbers 34, 35, 23, 26, 40, 27 and 39 is 224.

2. 2

Divide the sum of all values by the number of values in the data set to obtain the average value. In the example, the average is 224 / 7 = 32. Store or otherwise remember the sum and the number of values.

3. 3

Add any newly recorded values to the previous sum of numbers. For a new value = 38 added to the previous data set, the new sum is 262. There are now eight values, so the new average = 262 / 8 = 32.75. Continue adding new values to the previous sum, and continue to increment the count of variables each time.

1. 1

Select a window size. For example, from a set of seven numbers (34, 35, 23, 26, 40, 27, 39) a reasonable window size could be 5. Sum the 5 most recently recorded numbers: 23 + 26 + 40 + 27 + 39 = 155.

2. 2

Divide the sum by 5, the number of values in the window. Using the example, 155 / 5 = 31.

3. 3

Add any new values to the end of the list of numbers, such as a new value of 38. Sum the 5 values most recently recorded, in this case 26 + 40 + 27 + 39 + 38 = 170.

4. 4

Divide the sum by 5, because the number of values in the window has not changed. In our example, 170 / 5 = 34.

5. 5

Repeat, each time discarding the oldest value from the window and adding in the newest value. Always divide by the same number, the window "length."

#### Tips and warnings

• A cumulative running average will always change toward the most recently recorded number. The larger the count of variables, the less a cumulative average will change.
• A moving average is intended to measure short-term trends. Moving averages are often used when measurements are made at regular time intervals.

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