How to calculate the mean — step by step (with a worked example)
The mean (the arithmetic average) is the sum of all values divided by their count. Alongside it are two more measures of centre: the median (the middle of the ordered list) and the mode (the most frequent value). Worked example: 4, 8, 15, 16, 23, 42 → mean 18. Fits descriptive statistics from Grade 8 / Year 9 onward.
Quick answer
To calculate the mean, add all the numbers and divide by how many there are. Example: 4, 8, 15, 16, 23, 42 — the sum is 108, divided by 6 gives a mean of 18. The median (the middle value of the ordered list) is 15.5 here, and there is no mode because no value repeats.
At a glance
| Example | (4 + 8 + 15 + 16 + 23 + 42) ÷ 6 |
|---|---|
| Method | Sum divided by count |
| Steps | 4 |
| Mean | = 18 |
| Median / mode | Median 15.5 — no mode |
| Grade level | Grade 8 (ages 13–14) |
Worked example: mean of 4, 8, 15, 16, 23, 42
We add the six numbers to get 108, then divide by 6.
The 4 steps to calculate the mean
These four steps work for any list of numbers, no matter how long.
Step 1 · Start
4, 8, 15, 16, 23, 42Six values, so the count is n = 6.Step 2 · Sum
4 + 8 + 15 + 16 + 23 + 42 = 108Adding all the values gives a sum of 108.Step 3 · ÷ 6
108 ÷ 6Divide the sum by the number of values.Step 4 · Result
= 18The mean of the list is 18.
Why “sum divided by count” gives the average
The mean spreads the total sum evenly across all the values: if every value had the same share, it would be exactly this average. That is why the mean always lies between the smallest and largest value. Because every value counts, it is sensitive to outliers — a single extreme value pulls it up or down. In those cases the median often describes the centre more realistically.