Skip to content

Mean Formula

All Calculators

The mean is the average you already know: add the values, divide by how many there are. Written down, it is one line of algebra, which is why the mean is the measure most coursework asks for first.

The formula

x̄ = Σx ÷ n

  • Σx is the sum of all the values.
  • n is how many values there are, counting repeats.
  • x̄ is the mean, read as “x bar”.

Worked example: whole numbers

For the test scores 12, 15, 15, 18, 20:

  1. Add them: 12 + 15 + 15 + 18 + 20 = 80.
  2. Count them: n = 5.
  3. Divide: 80 ÷ 5 = 16.

The mean score is 16.

Worked example: negative numbers

For −5, 10, −15, 20:

  1. Add them, keeping the signs: −5 + 10 − 15 + 20 = 10.
  2. Count them: n = 4.
  3. Divide: 10 ÷ 4 = 2.5.

Only the signs need care. Adding a negative number lowers the total, and the arithmetic is otherwise identical.

Worked example: decimals

For 1.5, 2.5, 3.5:

  1. Add them: 1.5 + 2.5 + 3.5 = 7.5.
  2. Count them: n = 3.
  3. Divide: 7.5 ÷ 3 = 2.5.

Worked example: with a frequency table

If the value 12 appears 3 times, 15 appears 2 times and 18 appears once, there are six values in total with a sum of 36 + 30 + 18 = 84, so the mean is 84 ÷ 6 = 14.

Common mistakes

  • Dividing by the number of different values instead of the number of values. Both 15s count, so n is 5, not 4.
  • Losing a minus sign while adding. Write the sum out with the signs before you total it.
  • Rounding too early. Keep full precision until the end, then round to the number of decimal places your work requires.
  • Using the mean when the data is skewed. With a few very large values the median usually describes the data better.
Scroll to Top