Table of Contents
Introduction to Weighted Mean
Weighted Mean – Definition: The weighted mean is a type of arithmetic mean, which is calculated by multiplying each value in a data set by a weight and then adding up the results. The weighted mean is often used when the values in a data set are not all of equal importance. The weight can be thought of as a measure of the importance of each value in the data set.
Weight Definition
There is no one-size-fits-all definition of weight, as it can mean different things to different people. In general, weight is a measure of how much mass an object has. It can calculated by multiplying an object’s mass by the gravitational force exerted on it. Weight can also thought of as a force that resists movement, or the amount of mass needed to produce a certain acceleration.
What Weighted Mean?
The weighted mean is a calculation that takes into account the relative importance of each number in a set. To calculate the weighted mean, you first need to determine the weight of each number. The weight of a number is the number’s importance divided by the total number of numbers in the set. Then, you add up the weights of all the numbers in the set, and divide the total weight by the total number of numbers. The weighted mean is the result of this calculation.
Define Weighted Mean
The weighted mean is a mathematical calculation that takes into account the relative importance of each number in a set. The calculation performed by multiplying each number in the set by a weight, and then adding the results. The weighted mean then calculated by dividing the sum by the sum of the weights.
Weighted Mean Formula
The weighted mean formula used to calculate the average of a set of numbers, where some numbers are given more weight than others. weighted mean calculated by multiplying each number in the set by its weight, and then adding all of the weighted values together. The weighted mean formula is:
(Weighted Mean = \frac{1}{N}\sum_{i=1}^{N}w_i x_i)
where:
(Weighted Mean\) is the weighted mean
(N\) is the number of data points
(w_i\) is the weight of data point \(i\)
(x_i\) is the data point \(i\)
Uses of Weighted Means
Weighted means often used in surveys, where they can used to adjust for the non-response bias of a survey. This done by giving different weights to different respondents, depending on how likely they to respond. This can give a more accurate estimate of the population mean than would obtained if all respondents given the same weight.
Weighted means can also used to adjust for the clustering of data. This done by giving different weights to different data points, depending on how close they are to other data points. This can give a more accurate estimate of the population mean than would obtained if all data points given the same weight.
Solved Example
Example: Weighted Mean In a class of 30 students, the average (mean) score on a test is 75. The average score of the male students is 80 and the average score of the female students is 70. Find the weighted mean score.
Ans. The weighted mean score is 76.7.
Helpful Resources
- NCERT Solutions for Class 6
- NCERT Solutions for Class 7
- NCERT Solutions for Class 8
- NCERT Solutions for Class 9
- NCERT Solutions for Class 10
- NCERT Solutions for Class 11
- NCERT Solutions for Class 12
Frequently Asked Questions (FAQs)
What does weighted mean means?
Weighted mean means giving different values or items varying levels of importance or weight in a calculation.
How do you explain weighted mean in research?
In research, the weighted mean accounts for the significance of individual data points by assigning weights, often used in aggregating survey results.
How do you calculate weighted mean?
To calculate the weighted mean, multiply each value by its corresponding weight, sum these products, and divide by the total weight.
What is the weighted mean difference?
The weighted mean difference measures the impact of different factors on the mean, often used in statistical analysis to assess the influence of variables.
