Average

Mathematics · 4 min read · Sunitha Rao

Arithmetic mean, weighted average and the deviation shortcut.

The average of a set is its total divided by the number of items. Almost every exam question is really about the total: if the average of 5 numbers is 20, the total is 100, and that total is what you manipulate.

When one value is replaced, the change in average multiplied by the count gives the change in total. If the average of 10 students' marks rises by 2 after correcting one score, that score was understated by 20.

For consecutive numbers the average is simply the middle term, so the average of the first n natural numbers is (n + 1) / 2.

Important points

  • Average = sum of observations / number of observations.
  • Sum = average x count. Convert to totals first.
  • Average of first n natural numbers = (n+1)/2.
  • Weighted average = (n1a1 + n2a2) / (n1 + n2).

Key formulas

Average = Sum / Count

Weighted average = (n1a1 + n2a2)/(n1 + n2)

Examples

  1. Average of the first 10 natural numbers = 11/2 = 5.5.
  2. Average of 5 numbers is 20; adding a sixth number 26 gives a new average of 21.

Practise Average questions →