Weighted Average Calculator

Weighted Average Calculator

Weighted average calculator is used to calculate the weighted average of the same objects with different sizes and weights.

What is the Weighted Average?

A weighted average is an average in which a weight is applied to each quantity to be averaged. The average relative relevance of each quantity is determined by these weightings. The equivalent of weightings is including that many comparable items of the same value in the average.

Formula:

Weighted Average = sum of all (weights × values) / sum of all weights

Weighted Average = w₁x₁ + w₂x₂ + w₃x₃ + ... + w_n x_n / w₁ + w₂ + w₃ + ... + w_n

How to calculate the weighted average?

Example 1:

Weighted Average =?

Weights = 13,14,15,16,17

Values = 23,24,25,26,27

Solution:

Step 1: Take the formula of the weighted average.

Weighted Average = w₁x₁ + w₂x₂ + w₃x₃ + ... + w_n x_n / w₁ + w₂ + w₃ + ... + w_n

Step 2: Put the values and weights into the above formula.

Weighted Average = (23 * 13) + (24 * 14) + (25 * 15) + (26 * 16) + (27 * 17) / (13 + 14 + 15 + 16 + 17)

                              = 299 + 336 + 375 + 416 + 459 / 13 + 14 + 15 + 16 + 17

                              = 1885 / 75

                              = 25.1333

Example 2:

Weighted Average =?

Weights = 125,126,127,128,129

Values = 33,45,56,67,73

Solution

Step 1: Take the formula of the weighted average.

Weighted Average = w₁x₁ + w₂x₂ + w₃x₃ + ... + w_nx_n / w₁ + w₂ + w₃ + ... + w_n

Step 2: Put the values and weights into the above formula.

Weighted Average = (33 * 125) + (45 * 126) + (56 * 127) + (67 * 128) + (73 * 129) / (125 + 126 + 127 + 128 + 129)

                              = 4125 + 5670 + 7112 + 8576 + 9417 / (125 + 126 + 127 + 128 + 129)

                              = 34900 / 635

                              = 54.9606

Here are some other results of the weighted average calculator