104 LearnersLast updated on August 9th, 2025
Math Formula for Weighted Mean
In statistics, the weighted mean is a measure of central tendency that accounts for the importance or frequency of each value in a data set. In this topic, we will learn the formula for calculating the weighted mean and understand its application.
List of Math Formulas for Weighted Mean
The weighted mean provides a more accurate measure of central tendency when certain values are more significant than others. Let’s learn the formula to calculate the weighted mean.
Math Formula for Weighted Mean
The weighted mean accounts for the significance or frequency of each value. It is calculated using the formula:
Weighted Mean = (Σw_i * x_i) / Σw_i
where w_i is the weight of each value, x_i is each value, and Σw_i is the sum of all weights.
Importance of the Weighted Mean Formula
In math and real life, the weighted mean formula helps analyze datasets where not all values are equally important. Here are some key points about the weighted mean:
- It is used to find an accurate average in datasets with varying importance.
- The weighted mean helps in financial calculations like average returns on investments with different sizes.
- It is applicable in survey analysis where responses have different levels of significance.
Tips and Tricks to Memorize the Weighted Mean Formula
Students may find the weighted mean formula tricky. Here are some tips to master it:
- Remember that weights represent importance or frequency in the dataset.
- Practice with real-life data, such as calculating the average grade where assignments have different weightings.
- Use visual aids like charts to understand how weights affect the mean.
Real-Life Applications of the Weighted Mean Formula
The weighted mean is widely used in various fields to interpret data accurately. Some applications include:
- In education, calculating the final grade considering different weightings for assignments and exams.
- In finance, determining the average return on a portfolio with investments of different sizes.
- In market research, analyzing survey data where responses have different levels of impact.
Common Mistakes and How to Avoid Them While Using the Weighted Mean Formula
Students make errors when calculating the weighted mean. Here are some mistakes and ways to avoid them:
Mistake 1
Ignoring Weights in Calculation
A common mistake is treating all values as equally important. To avoid this, ensure each value is multiplied by its corresponding weight before summing.
Mistake 2
Incorrectly Adding Weights
Errors occur when weights are not counted correctly. Double-check the sum of the weights to ensure accuracy.
Mistake 3
Confusing Weighted Mean with Arithmetic Mean
Students sometimes confuse the weighted mean with the arithmetic mean. Remember that the weighted mean adjusts for the importance of each value, unlike the arithmetic mean.
Mistake 4
Using Incorrect Weights
Using inappropriate or arbitrary weights can lead to incorrect results. Ensure weights accurately reflect the importance or frequency of each value.
Mistake 5
Misinterpreting Results
Misinterpretation arises when the significance of weights is not understood. Always consider the context and implications of the weights used.
Examples of Problems Using the Weighted Mean Formula
Problem 1
A student has scores of 80, 85, and 90 in three assignments with weights 1, 2, and 3, respectively. Find the weighted mean score.
The weighted mean score is 86.67
Explanation
To find the weighted mean, calculate:
Weighted Mean = (80*1 + 85*2 + 90*3) / (1 + 2 + 3) = (80 + 170 + 270) / 6 = 520 / 6 = 86.67
Problem 2
A portfolio consists of three investments with returns of 5%, 7%, and 10%, and weights of 2, 3, and 5. What is the weighted mean return?
The weighted mean return is 8.3%
Explanation
To find the weighted mean return, calculate:
Weighted Mean = (5*2 + 7*3 + 10*5) / (2 + 3 + 5) = (10 + 21 + 50) / 10 = 81 / 10 = 8.3%
Problem 3
Three projects have completion times of 4, 6, and 8 weeks with weights of 3, 2, and 1, respectively. Find the weighted mean completion time.
The weighted mean completion time is 5.33 weeks
Explanation
To find the weighted mean completion time, calculate:
Weighted Mean = (4*3 + 6*2 + 8*1) / (3 + 2 + 1) = (12 + 12 + 8) / 6 = 32 / 6 = 5.33 weeks
Problem 4
Calculate the weighted mean of scores 72, 88, and 95 with weights 1, 4, and 5.
The weighted mean is 89.1
Explanation
To find the weighted mean, calculate:
Weighted Mean = (72*1 + 88*4 + 95*5) / (1 + 4 + 5) = (72 + 352 + 475) / 10 = 899 / 10 = 89.1
Problem 5
A survey has responses with scores 3, 5, and 7, with weights 2, 3, and 5. What is the weighted mean score?
The weighted mean score is 5.7
Explanation
To find the weighted mean score, calculate:
Weighted Mean = (3*2 + 5*3 + 7*5) / (2 + 3 + 5) = (6 + 15 + 35) / 10 = 56 / 10 = 5.7
FAQs on Weighted Mean Formula
1.What is the weighted mean formula?
2.How does the weighted mean differ from the arithmetic mean?
3.When should you use the weighted mean?
4.How do you choose weights for the weighted mean?
5.Can the weighted mean be used for all types of data?
Glossary for Weighted Mean Formula
- Weighted Mean: A measure of central tendency that accounts for the significance or frequency of values.
- Weights: Values representing the importance or frequency of each data point in a dataset.
- Arithmetic Mean: A measure of central tendency calculated by dividing the sum of values by the number of values.
- Central Tendency: A statistical measure that identifies a single value as representative of a dataset.
- Dataset: A collection of data points or values that are analyzed for statistical purposes.
Jaskaran Singh Saluja
About the Author
Jaskaran Singh Saluja is a math wizard with nearly three years of experience as a math teacher. His expertise is in algebra, so he can make algebra classes interesting by turning tricky equations into simple puzzles.
Fun Fact
: He loves to play the quiz with kids through algebra to make kids love it.
