What is the difference between "weighted mean" and "arithmetic mean?"
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The weighted mean and arithmetic mean are both measures of central tendency used to find the average value in a data set. However, they differ in terms of how they handle the individual values within the set.
The arithmetic mean, also known as the simple average, is calculated by adding up all the values in the data set and dividing the sum by the total number of values. It treats each value equally and assumes that each value has the same importance or weight.
On the other hand, the weighted mean takes into account the importance or weight of each value within the data set. Each value is assigned a weight, which represents its relative importance. The weighted mean is calculated by multiplying each value by its corresponding weight, summing up these weighted values, and dividing by the sum of the weights.
To understand the difference between the two, let's consider an example:
Suppose you want to calculate the average score of five students in a class. For the arithmetic mean, you simply add up the scores of all students and divide by 5 (assuming equal weight for each student's score).
For the weighted mean, let's say you have additional information that two students have been given double importance because they performed exceptionally well. In this case, you assign a weight of 1 for three students and a weight of 2 for the two exceptional students. You multiply each score by its respective weight, add up the weighted scores, and divide the sum by the total sum of the weights (which is 7 in this case).
In summary, the difference between the weighted mean and arithmetic mean lies in the consideration of weights for individual values. The arithmetic mean treats all values equally, while the weighted mean assigns different weights to reflect the relative importance or significance of the values.