Тарифы

Калькулятор взвешенного среднего

Этот калькулятор находит среднее, когда одни значения важнее других, например оценки с разными весами. Введите значения и их веса; он умножает, складывает и делит, показывая каждый шаг.

Разделяйте значения запятыми или пробелами.
Весами могут быть проценты, кредиты или количества.

Результат

Введите значения и нажмите «Вычислить», чтобы увидеть результат.

Формула

xˉw=∑wixi∑wi\bar{x}_w = \frac{\sum w_i x_i}{\sum w_i}

Multiply each value by its weight, add the results, then divide by the total weight.

Как пользоваться этим калькулятором

  1. Enter the values, then their weights in the same order.
  2. Weights do not need to add up to 1 or 100: the calculator divides by their total.
  3. Press Calculate to see the weighted average and the working.

Разобранные примеры

Marks 80, 90 and 70 with weights 2, 3 and 5

80 × 2 + 90 × 3 + 70 × 5 = 160 + 270 + 350 = 780.

The weights add up to 10, so the weighted average is 780 ÷ 10 = 78.

Percent weights: 72 (40%) and 85 (60%)

72 × 40 + 85 × 60 = 2880 + 5100 = 7980.

7980 ÷ 100 = 79.8.

Частые ошибки

  • Taking the ordinary mean, which treats every value as equally important.
  • Dividing by the number of values instead of the total weight.
  • Listing weights in a different order from the values.

Частые вопросы

How do you calculate a weighted average?

Multiply each value by its weight, add these products, and divide by the sum of the weights.

Do the weights have to add up to 100%?

No. Dividing by the total weight takes care of it: weights 2, 3, 5 work the same as 20%, 30%, 50%.

When is a weighted average used?

Course grades with weighted assignments, grade point averages with credit hours, and averaging prices bought in different quantities.