Weighted Average Calculator: Calculate Weighted

A weighted average calculator is an online tool which allows you to calculate the average of several values, with the ability to assign weights to each value.

Weighted averages are commonly used by students, investors, businesses, statisticians and in general life. Teachers can calculate a students overall grade by assigning different percentages to different parts such as homework, quizzes, projects & exams. Investors can calculate the average purchase price of stocks by assigning weights.

For example, if a student scores 85 for homework, 90 for quizzes and 75 for their final exam, with homework being worth 20%, quizzes worth 30% and exams worth 50% then their final grade can be calculated.

The CostCalco weighted average calculator makes calculating this easier by allowing you to input the values and weights.

This weighted average calculator can be used by students, teachers, business owners, investors and data analysts in the United States.

How To Use The Weighted Average Calculator

The weighted average calculator is easy to use. Simply follow the steps below to calculate your weighted mean.

1. Input Values

Add your numbers/scores/prices/measurements.

2. Input Weights

Input the weight for each value. This could be percentages, quantities or any other numerical factor.

3. Add More

If you have more values add more rows.

4. Double Check

Ensure that all of your values have been given a weight and that they have been input correctly.

5. Calculate

Click calculate.

6. View Results

The weighted average will be shown.

Example

Say you have the following test scores:

Test 1 – 80 (Weight 20%)

Test 2 – 90 (Weight 30%)

Test 3 – 85 (Weight 50%)

Input into the calculator.

Result

85

As you can see the calculator automatically works out the weighted average by multiplying the score by the weight and dividing by the total weights.

Weighted Average Calculator Formula

The weighted average can be calculated by multiplying each value by its weight, adding all the weighted values together and dividing by the total weight.

The formula is:

Weighted Average =
$$
\\frac{\\sum_{i=1}^{n}(x_i \\times w_i)}
{\\sum_{i=1}^{n}w_i}
$$
Where,
\\(x_i\\) = Value
\\(w_i\\) = Weight
\\(n\\) = Number Of Values
\\(\\sum\\) = Sum Of Values/Weights
If weights are in percentages
WA =
$$
\\frac{(x_1w_1)+(x_2w_2)+…+(x_nw_n)}{100}
$$

For example, if an exam score is worth 60% and a project is worth 40%, multiply the scores by the percentages.

Note: If your weights don’t add up to 100%, use the general weighted average formula and divide by the total weight.

Examples

Let’s look at some examples of how to calculate a weighted average.

Example 1 – Students Grade

Say a student had the following scores:

Assessment Score Weight

Homework 85 20%

Quizzes 90 30%

Exam 80 50%

Step 1 – Multiply Scores By Weights:

Homework: 85 × 0.20 = 17

Quizzes: 90 × 0.30 = 27

Exam: 80 × 0.50 = 40

Step 2 – Add The Weighted Values:

17 + 27 + 40 = 84

Result

84

The students weighted average grade is 84%.

Example 2 – Average Stock Purchase Price

An investor buys shares in a company at different prices:

Purchase Share Price Quantity

Purchase 1 $50 10

Purchase 2 $60 20

Purchase 3 $55 30

The quantity represents the weight.

Step 1 – Multiply Prices By Quantity:

i=10__500
i=11__1,200
i=12__1,650
Step 2 – Add The Weighted Values:
i=13__1,200 + i=14__3,350
Step 3 – Total Quantity:
i=15__ shares
Step 4 – Calculate Weighted Average:
i=16__55.83

Result

$55.83 Per Share

The investors weighted average purchase price would be around $55.83 per share (not including any fees or costs).

Example 3 – Weighted Average With Different Weights

A business wants to work out the weighted average for three different scores for customer satisfaction:

Customer Group Score Weight

Group A 75 2

Group B 85 3

Group C 95 5

WA =
$$
\\frac{(75\\times2)+(85\\times3)+(95\\times5)}{2+3+5}
$$
WA =
$$
\\frac{150+255+475}{10}
$$
WA =
$$
\\frac{880}{10} = 88
$$

Result

88

This demonstrates how the weighted average takes into account the different weights.

Understanding Your Results

Your results from the weighted average calculator show the average value taking into account the weights.

Unlike an arithmetic average, weighted values with higher weights will have more influence.

Take the table below:

Value Weight Weighted Value

70 20% 14

80 30% 24

90 50% 45

Total 100% 83

Weighted Average: 83

This means that the overall average will be 83.

Weighted Value: Shows how much each individual value contributes to the overall average.

Total Weight: The total weight of all values.

Weighted Average: The calculated value.

Values with higher weights will have more influence on the overall result.

Factors That Influence Results

There are several factors that can influence the result.

1. Values

The values you put into the calculator will influence the result. Higher or lower values will increase or decrease the weighted average.

2. Weights

Values with higher weights will have more influence on the result. If the wrong weights are applied this can give misleading results.

3. Total Weight

The total weight will be used as the denominator. The calculator divides the total weighted value by the total weight.

4. Percentage Or Numerical Weights

You can input either percentages or numerical weights. Just ensure the weights are interpreted the same way.

5. Number Of Values

Adding more values and weights can change the overall average.

6. Accurate Data

If you put incorrect values or leave weights blank this can cause inaccurate results.

7. Weight Distribution

If most of the weight is assigned to one value this will have more influence on the result.

Benefits & Uses Of A Weighted Average Calculator

A weighted average calculator can be useful in many industries.

1. Education

Teachers and students can calculate final grades by assigning weights to homework, quizzes, assignments, projects and exams.

2. Investments

Investors can calculate the average purchase price of stocks based on how many they have purchased.

3. Businesses

Businesses can calculate an overall score for sales, customer satisfaction, productivity and performance based on how important they are.

4. Finance

Finance professionals can use weighted averages when analysing portfolios, interest rates and other financial figures.

5. Inventory

Retailers can calculate a weighted average cost of inventory based on how much they have purchased.

6. Statistics

Researchers can calculate an overall score from surveys, samples and statistics by assigning weights.

7. Employee Performance

Organisations can calculate employee performance scores by assigning weights to productivity, attendance, quality etc.

8. Students, Analysts & Professionals

Students, analysts and professionals can use weighted averages to provide meaningful summaries from data sets where the observations aren’t equal.

Accuracy, Assumptions & Limitations

The weighted average calculator will provide accurate results if the values and weights are correct.

However there are some assumptions and limitations.

Correct Weights: The result will only be accurate if the correct weights are applied.

Total Weight > 0: The total weights must be greater than 0. If the total is 0 then a weighted average cannot be calculated.

• Consistent Units: All values should be in the same unit. Don’t mix different currencies unless they have been converted.
• Percentages: If using percentages ensure they are interpreted the same way. They don’t need to add up to 100% if using the general formula.
• Negative Values: These may be mathematically correct but will depend on what they represent.
• Missing Data: Missing values/weights can impact the calculation.
• Rounding: The result may be rounded to a certain number of decimal places. This can cause slight discrepancies.
• Appropriate Weights: The calculator will not decide whether the weights you have chosen are appropriate. You must choose them based on your requirements.

A weighted average will not automatically give you an indication of variability and why individual values differ. Further measures may be required for further statistical analysis.

FAQs

1. What Is A Weighted Average Calculator?

A weighted average calculator is an online tool which calculates an average by taking into account the importance/weight of each value. It does this by multiplying each value by its weight, adding the values together and dividing by the total weight.

2. What Is The Difference Between An Average And A Weighted Average?

An average gives equal importance to all values whereas a weighted average gives different importance to values based on their weight. A weighted average can be useful when calculating students grades as final exams are worth more than homework.

3. Can I Calculate A Weighted Average If My Weights Don’t Add Up To 100%?

Yes. You can still calculate a weighted average if your weights don’t add up to 100%. Use the general formula by dividing the total weighted values by the total weights. For example, if the weights were 2, 3 & 5 then they can be used as is.

4. How Do I Calculate A Weighted Average In Excel?

You can calculate a weighted average in excel using the SUMPRODUCT & SUM functions. For example if your values are in column A (A2:A4) and your weights are in column B (B2:B4) then use the following:
=SUMPRODUCT(A2:A4,B2:B4)/SUM(B2:B4)
This multiplies each value by its weight and divides by the total weights.

5. Can A Weighted Average Be Higher/Lower Than An Average?

Yes. Depending on the weights chosen a weighted average can be higher or lower than an average. If higher values have higher weights then the weighted average will generally be higher. If lower values have higher weights then it may be lower.