Weighted Average

The weighted average, also known as the weighted mean, is easily computed by our weighted average calculator. This statistical measure takes into account the importance or weight of each number in a dataset. It is calculated by multiplying each number by its corresponding weight, summing these products, and then dividing by the total sum of weights. This method gives more significance to certain numbers based on their importance in the dataset.

Weighted Average Formula

To calculate weighted average, multiply each number by its weight, sum the results, and divide by the total weights. You can also use the weighted average formula for the same,
A = w 1 x 1 + w 2 x 2 + . . + w n x n w 1 + w 2 + . . + w n
A - Weighted average | x1, x2,..., xn - Numbers | w1, w2,..., wn - Weights

Applications of Weighted Average

Weighted averages are extensively used in various real world scenarios where certain data points carry more significance than others. Some common applications include:
Grades and Courses: Calculating the weighted average grade in a course based on different assignments, exams, and their respective weights.
Financial Investments: Determining the weighted average return on investment (ROI) considering the varying amounts invested and their durations.
Product Reviews: Computing a weighted average rating for a product based on customer reviews and the weight assigned to each review.
Exam Scores: Calculating the weighted average score of a student across multiple exams with different point values.

Weighted Average Examples

Here are the weighted average examples to calculate weighted average in different set of data.
Example 1: Average Time Spent on Different Tasks at Work
Data: 5 hours on meetings, 3 hours on project work, 2 hours on emails, 1 hour on administrative tasks
Weight: 2, 4, 3, 1
Weighted Average: 2.9 hours
Example 2: Average Scores in Exams
Data: 85, 90, 78, 92, 88
Weights: 3, 2, 4, 5, 1
Weighted Average: 72.13
Example 3: Average Daily Temperature
Data: 70°F, 75°F, 68°F, 72°F, 74°F
Weights: 1, 2, 3, 4, 5
Weighted Average: 72.13°F
Example 4: Average Weekly Spending
Data: 50 hours, 60 hours, 45 hours, 70 hours, 55 hours, 65 hours, 40 hours
Weights: 2, 3, 1, 4, 5, 2, 3
Weighted Average: 56.5 hours
Example 5: Average Height of Students
Data: 150 cm, 160 cm, 155 cm, 165 cm, 170 cm
Weights: 1, 2, 3, 4, 5
Weighted Average: 163 cm

Weighted Average Calculator FAQ

What are weights in a weighted average?
Weights in a weighted average represent the relative importance or contribution of each data point to the overall average. Higher weights indicate that a data point has a greater impact on the average.
Can weights be negative in a weighted average calculation?
No, weights in a weighted average calculation should be positive. Negative weights would lead to mathematically incorrect results.
What is the difference between a weighted average and a regular average?
A regular average treats all data points equally, whereas a weighted average assigns different weights to data points based on their importance. As a result, a weighted average can reflect the impact of certain data points more accurately.
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