套餐

加权平均数计算器

这个计算器在某些数值比其他数值更重要时求平均数，例如权重不同的成绩。输入数值及其权重；它会相乘、相加再相除，并显示每一步。

用逗号或空格分隔数值。
权重可以是百分比、学分或次数。

结果

输入数值并点击“计算”查看结果。

公式

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.

如何使用此计算器

  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.

例题

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.

常见错误

  • 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.

常见问题

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.