Question

Basic Computation: Weighted Average Find the weighted average of a data set where 10 has a weight of $5 ; 20$ has a weight of $3 ; 30$ has a weight of 2

Name: Problem 24, Chapter 3: Understandable Statistics Concepts and Methods
Uploaded: 2021-04-05T22:53:19-08:00
Duration: 1 min 20 s
Channel: Jerrah Biggerstaff
Description: Basic Computation: Weighted Average Find the weighted average of a data set where 10 has a weight of 5 ; 20 has a weight of 3 ; 30 has a weight of 2

   Basic Computation: Weighted Average Find the weighted average of a data set where
10 has a weight of $5 ; 20$ has a weight of $3 ; 30$ has a weight of 2

Understandable Statistics Concepts and Methods

Charles Brase,… 12th Edition

Chapter 3, Problem 24

Instant Answer

Solved by Expert Jerrah Biggerstaff

04/05/2021

Step 1

This is done by multiplying each data point by its weight and then adding all these products together. In this case, we have: \[10 \times 5 + 20 \times 3 + 30 \times 2\] Show more…

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Basic Computation: Weighted Average Find the weighted average of a data set where 10 has a weight of $5 ; 20$ has a weight of $3 ; 30$ has a weight of 2

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Key Concepts

Weighted Average

A weighted average is a method of calculating the mean of a dataset where each number is multiplied by a predetermined weight reflecting its importance. The final average is obtained by dividing the sum of these weighted values by the total of the weights, allowing more influential numbers to have a greater impact on the result.

Weighted Sum

The weighted sum involves multiplying each value in the dataset by its respective weight and then summing these products. It represents the numerator in the weighted average formula and is essential for aggregating the contributions of all weighted values.

Normalization

Normalization in the context of weighted averages refers to dividing the weighted sum by the total weight. This process ensures that the resulting average properly reflects the relative importance of each data point by scaling the sum of the weighted values to a comparable measure.

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