Average Calculator

Type up to five numbers. The calculator shows the mean (sum ÷ count), the sum, the count of numbers it used, and the median, the middle value once the numbers are sorted. The defaults, 10, 20 and 30, give a mean of 20, a sum of 60, a count of 3 and a median of 20.

Any box left empty is ignored, including the first three. Clearing Number 1 and filling Number 5 works fine: 20, 30 and 5 give a count of 3 and a mean of 18.33. Check the count line to confirm the calculator used the numbers you meant.

Scores of 80 and 90 with the third box empty average 85. Type 0 in that box and the average drops to 56.67, the count becomes 3 and the median 80.

Decide which one you mean before you enter it. A test that was excused should be left blank. A test that was missed and scored as zero should be typed as 0, because it really does pull the average down.

The mean uses every value, so one extreme number moves it a lot. Response times of 12, 15, 14, 13 and 96 seconds have a mean of 30, a number none of them is close to. The median is 14, which describes a typical response much better.

Use the median when a few unusual values could distort the picture, as with prices, incomes or waiting times. Use the mean when every unit matters to the total, as with average spend per order when you're forecasting revenue. With an even count, the median is the average of the two middle values: 10, 20, 30 and 40 give 25.

The calculator gives every number equal weight. That's wrong when the numbers are themselves averages or rates for groups of different sizes.

• Class averages: a class of 20 averaged 70 and a class of 30 averaged 80. Entering 70 and 80 gives 75. The true average across all 50 students is (20 × 70 + 30 × 80) ÷ 50 = 76.
• Speeds: you drive somewhere at 30 mph and back the same distance at 60 mph. Entering 30 and 60 gives 45, but your average speed for the trip is 40 mph, because you spent twice as long on the slow leg.

The fix is always the same: go back to the totals (total points ÷ total students, total distance ÷ total time).

Split the list into batches of up to five and add the sums, not the means. For 4, 8, 15, 16, 23, 42, 7 and 9:

1. First five: sum 66, count 5.
2. Last three: sum 58, count 3.
3. Overall mean: (66 + 58) ÷ 8 = 15.5.

Averaging the two batch means (13.2 and 19.33) would give 16.27, which is wrong for the same reason as the class example. The median can't be combined from batches, so sort the full list yourself to find it.