During your schooling, you will inevitably want to calculate an average at one point or another. For academic, professional or even personal reasons, calculating an average is a basic mathematical operation that you must know how to master. There are two main types of averages: the simple average and the weighted average. Business Cool deciphers all their secrets for you!
Throughout this article, you will find explanations and some examples for each of the averages that we will decipher, from the simple, weighted average with coefficient, to the one that you can create in Excel and many others. So, calculating an average will no longer have any secrets for you.
How to calculate a simple average (general average)?
A simple average, also called an arithmetic average, is generally the one we use when studying in college or high school. In fact, this average is called “simple” because all the values have the same weight. In order to calculate this average, simply add all the values together and then divide the result obtained by the total number of values.
The formula for this average is as follows: Sum of values / total number = Average. For example, if during the first quarter of the second year you obtained the following grades:
- Mathematics: 12
- LV1: 14
- LV2: 10
- History: 15
- EPS: 11
- SVT: 8
- Physics-Chemistry: 17
- French: 4
The calculation to be made is as follows: 12+14+10+15+11+8+17+4 = 91 ; 91/8 = 11.37
So you got the average of 11.37.
How is a weighted average (with coefficient) calculated?
When calculating a weighted average, this necessarily involves coefficients. This is the case for the baccalaureate grades. This is the reason why this calculation is mainly used by secondary school or university students. A weighted average – or cumulative grade point average – will make it possible to calculate the average over all courses, while taking into account the number of times a grade counts.
For example, if your baccalaureate results are as follows:
- Mathematics: 11 / coefficient 4
- History-Geography: 6 / coefficient 3
- EPS: 15 / coefficient 2
- Physics-Chemistry: 17 / coefficient 3
The calculation to be made is as follows: (11 x 4) + (6 x 3) + (15 x 2) + (17 x 3) / (4 + 3 + 2 + 3) = 143 / 12 = 11.92
Calculating an average in Excel: how does it work?
If you want to calculate an average on Excel, nothing could be simpler! To start, you need to use a dedicated function. Calculating an average is done with the =AVERAGE function. In fact, if you want to calculate an average of numbers located in cells ranging from A1 to A50, you must then select all of these cells after entering =AVERAGE in the function bar above the table.
If you want to calculate a weighted average, you need to use the formula from the latter seen above and thus replace the value numbers with the corresponding cell numbers. So you need to create a table with a value column and another for the coefficients.
How do I calculate an average out of 20 and out of 10?
To calculate an average out of 20 and out of 10, nothing could be simpler! If in a subject you have obtained several marks, some out of 10 and others out of 20, you simply need to reduce all of your marks to marks out of 20 (by multiplying the one marked out of 10 by 2).
For example, in your Physics-Chemistry course, you obtained different grades:
- 7 out of 10 = 14 out of 20
- 13 out of 20
- 15 out of 20
- 4 out of 10 = 8 out of 20
- 2 out of 10 = 4 out of 20
The calculation to be made is therefore as follows: 14 + 13 + 15 + 8 + 4 = 54 ; 54 / 5 = 10.8
You therefore obtained an average in Physics Chemistry of 10.8 out of 20.
How to calculate the time average
Far from classes and closer to a physical activity, you may have to calculate an average time. If you are a runner and you want to know the average time you have achieved over a 15km over the past 10 days, you will need to take the average of the different times completed over this period:
- Day 1: 1h15
- Day 2: 1h12
- Day 3: 1h10
- Day 4: 1h06
- Day 5: 1h02
- Day 6: 59 minutes
- Day 7: 56 minutes
- Day 8: 58 minutes
- Day 9: 59 minutes
- Day 10: 55 minutes
First, you need to convert hours to minutes.
- Day 1: 1h15 = 75 minutes
- Day 2: 1h12 = 72 minutes
- Day 3: 1h10 = 70 minutes
- Day 4: 1h06 = 66 minutes
- Day 5: 1h02 = 62 minutes
- Day 6: 59 minutes
- Day 7: 56 minutes
- Day 8: 58 minutes
- Day 9: 59 minutes
- Day 10: 55 minutes
Once this step has been completed, all you have to do is calculate the average in the classic way, using the simple average formula seen above.
The calculation to be made is as follows: 75 + 72 + 70 + 66 + 62 + 59 + 56 + 58 + 59 + 55 = 632 ; 632 / 10 = 63.2
Over all of your 10 15km sessions, your average time is therefore 1 hour 3 minutes and 12 seconds.
How to calculate an average with values represented by intervals
Finally, it may happen that you need to calculate an average whose values are represented by intervals. To do this, you must calculate the center of each interval by taking the average of the two limits of the interval. Then, all you have to do is multiply the result obtained by the corresponding number. All you have to do is divide the result by the total number.
For example, a restaurateur wants to know the average daily amount spent in her establishment.
| Amount | Number of orders |
| Between 0 and 20€ | 40 |
| Between 20 and 50€ | 50 |
| Between 50 and 100€ | 20 |
| Between 100 and 200€ | 10 |
The calculation to be carried out and the following:
- 0 + 20 = 20; 20 / 2 = 10
- 20 + 50 = 70; 70 / 2 = 35
- 50 + 100 = 150; 150 / 2 = 75
- 100 + 200 = 300; 300 / 2 = 150
All you then need to do is take a weighted average as seen above:
(40*10) + (50*35) + (20*75) + (10*150) / 120 = 42.9
The average amount of daily expenses within his establishment is €42.9.
