What is an average?
The average, also called the mean, adds up all the numbers and divides by how many there are. The median is the middle number when they are in order, the mode is the number that appears most often, and the range is the largest number minus the smallest.
Source CDC · Principles of Epidemiology, Lesson 2, Section 6: Measures of central location ↗CDC · Principles of Epidemiology, Lesson 2, Section 7: Measures of spread ↗
How to calculate an average
Here it is with your numbers:
- Add the numbers: 27 + 31 + 15 + 30 + 22 = 125.
- Divide the total by how many numbers there are: 125 ÷ 5 = 25.
It means that if all 5 numbers were the same, each would be 25. The median, the middle number in order, is 27. No number appears more than once, so there is no mode.
A weighted average is for when some numbers count for more, like exam scores that are worth different shares of a grade. The weights decide how much each value counts.
Source Instructure (Canvas) · How weighted course grades are calculated ↗
Mean, median, mode and range
| Measure | Answer |
|---|---|
| Count | 5 |
| Sum | 125 |
| Mean (average) | 25 |
| Median | 27 |
| Mode | None |
| Smallest | 15 |
| Largest | 31 |
| Range | 16 |
Average examples
| Numbers | Answer |
|---|---|
| 27, 31, 15, 30, 22 (days) | Average 25 |
| 4, 23, 28, 31, 32 (years) | Median 28 |
| 0, 0, 1, 1, 2, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4 (doses) | Mode 3 |
| 75 × 20, 98 × 50, 87 × 30 (weighted) | Weighted average 90.1 |
FAQs
How do you calculate an average?
Add all the numbers, then divide by how many numbers there are. For 27, 31, 15, 30 and 22, the total is 125, and 125 ÷ 5 is 25, so the average is 25.
Source CDC · Principles of Epidemiology, Lesson 2, Section 6: Measures of central location ↗
How do you find the mean, median and mode?
Mean: add the numbers and divide by how many there are. Median: put them in order and take the middle one (with an even count, the average of the two middle ones). Mode: the number that appears most often. There is no mode if nothing repeats.
How do you calculate a weighted average?
Multiply each value by its weight, add those up, then divide by the total of the weights. Canvas’s example: 75 × 20, 98 × 50 and 87 × 30 add up to 9,010, and 9,010 ÷ 100 is 90.1.
Source Instructure (Canvas) · How weighted course grades are calculated ↗
Sources
- CDC: Principles of Epidemiology, Lesson 2, Section 6: Measures of central location
- CDC: Principles of Epidemiology, Lesson 2, Section 7: Measures of spread
- Instructure (Canvas): How weighted course grades are calculated