Question

A recent survey of a new diet cola reported the following percentages of people who liked the taste. Find the weighted mean of the percentages. $\begin{array}{ccc}{\text { Area }} & {\% \text { Favored }} & {\text { Number surveyed }} \\ \hline 1 & {40} & {1000} \\ {2} & {30} & {3000} \\ {3} & {50} & {800}\end{array}$

Name: Problem 25, Chapter 3: Elementary Statistics a Step by Step Approach
Uploaded: 2020-12-19T14:06:07-08:00
Duration: 2 min 46 s
Channel: Evelyn Cunningham
Description: A recent survey of a new diet cola reported the following percentages of people who liked the taste. Find the weighted mean of the percentages. Area % Favored Number surveyed 1 40 1000 2 30 3000 3 50 800

   A recent survey of a new diet cola reported the following percentages of people who liked the taste. Find the weighted mean of the percentages.
$\begin{array}{ccc}{\text { Area }} & {\% \text { Favored }} & {\text { Number surveyed }} \\ \hline 1 & {40} & {1000} \\ {2} & {30} & {3000} \\ {3} & {50} & {800}\end{array}$

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Chapter 3, Problem 25

Instant Answer

Solved by Expert Evelyn Cunningham

12/19/2020

Step 1

In this case, the percentages are our data points (X) and the number of people surveyed are the weights (W). Show more…

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A recent survey of a new diet cola reported the following percentages of people who liked the taste. Find the weighted mean of the percentages. $\begin{array}{ccc}{\text { Area }} & {\% \text { Favored }} & {\text { Number surveyed }} \\ \hline 1 & {40} & {1000} \\ {2} & {30} & {3000} \\ {3} & {50} & {800}\end{array}$

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Key Concepts

Weighted Mean

The weighted mean is an average that accounts for the relative importance or frequency of each data point. Instead of simply averaging values, each value is multiplied by a weight that represents its significance, and the sum of these products is then divided by the total of the weights.

Weighting Factor

A weighting factor is a number assigned to each data value that reflects its relative importance. In problems involving survey data, the number of respondents or frequency in each group serves as the weight, ensuring that groups with more data have a proportionally larger influence on the overall mean.

Data Aggregation in Surveys

Data aggregation in surveys involves combining results from different groups or areas while taking into account the size or frequency of each group. This is crucial for obtaining an overall measure that accurately reflects the contribution of each subgroup based on its sample size.

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