Weighted Average Calculator

What a weighted average means

A weighted average (or weighted mean) is an average in which some values count for more than others. Each value is paired with a weight that says how much influence it should have. The ordinary mean is the special case where every weight is the same.

Weighted averages appear whenever items are not equally important: a final exam worth more than a quiz, a purchase of 500 units that matters more than one of 5, or a survey group that is over- or under-represented in a sample.

The weighted average formula

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

weighted mean = (x₁w₁ + x₂w₂ + … + xₙwₙ) ÷ (w₁ + w₂ + … + wₙ)x are the values and w are their weights.

Dividing by the total weight is what lets the weights be written in any scale. Weights of 2, 3 and 5 give exactly the same answer as 0.2, 0.3 and 0.5, or 20, 30 and 50 percent: for the values 10, 20 and 30 all three sets produce 23. The weights do not need to add up to 100 or to 1.

How to use the calculator

1. Type or paste one pair per line: the value first, then its weight. Separate the two with a space, a tab or a comma, so data copied from a spreadsheet works unchanged.
2. Use a dot for decimals (0.25, not 0,25).
3. Press Calculate. The result is labeled “Weighted mean”.

You need at least two rows, and every row needs exactly two columns. A header line such as “x w” and blank lines are skipped. Negative values are allowed; if the weights add up to zero the mean is undefined and the calculator says so.

The answer is rounded to eight decimal places. Whole results appear bare (81), and shorter decimals are padded: two decimals or fewer to two places (1.50), three to six decimals to six places (0.125000), and seven or eight to eight places.

Example: a weighted course grade

A course counts assignments for 20 percent, the midterm for 30 percent and the final for 50 percent. A student scores 85, 72 and 90.

(85 × 20 + 72 × 30 + 90 × 50) ÷ (20 + 30 + 50) = 8,360 ÷ 100 = 83.6

Enter the three lines 85 20, 72 30 and 90 50 to get 83.60. The simple average of the three scores would be 82.33, lower because it treats the midterm as equal to the final. To find what score you need on a coming exam, use the final grade calculator, and for a running course total the grade calculator.

Example: average price paid

An investor buys 100 shares at 12.50, 250 shares at 11.80 and 50 shares at 13.25. The number of shares is the weight, and the price is the value.

(12.50 × 100 + 11.80 × 250 + 13.25 × 50) ÷ 400 = 4,862.50 ÷ 400 = 12.15625

The average cost per share is 12.15625, shown by the calculator as 12.156250. A plain average of the three prices would give 12.5167, which ignores that most of the money went into the cheapest lot.

Example: grade point average

A grade point average is a weighted mean in which credit hours are the weights. Four courses give grade points 4.0, 3.0, 3.7 and 2.0 for 3, 4, 3 and 2 credits.

(4.0 × 3 + 3.0 × 4 + 3.7 × 3 + 2.0 × 2) ÷ 12 = 39.1 ÷ 12 ≈ 3.2583

The calculator returns 3.25833333. The GPA calculator sets this up with letter grades.

Choosing the weights and the average

• Use quantities as weights when you are pooling groups, such as units sold or hours worked.
• Use importance as weights when you are scoring, such as grading categories or survey priorities.
• Keep all weights on the same scale. Mixing percentages with counts gives a meaningless answer.
• Negative weights are mathematically possible but rarely make sense, and they can push the mean outside the range of the values.

The weighted mean is an arithmetic average. For growth rates and ratios consider the geometric mean calculator, and for rates such as speed over equal distances the harmonic mean calculator. The mean calculator handles the equal-weight case.

Common mistakes

• Averaging the averages. The mean of two group means equals the overall mean only if the groups are the same size; otherwise weight by group size.
• Swapping the columns. The value goes first, the weight second.
• Dividing by the number of rows instead of by the total weight.
• Leaving out a category, so the weights no longer describe the whole course or portfolio.