WEEK 26-REAL-WORLD-APPLICATIONS-OF-WEIGHTED-AVERAGES

Objectives

Start

Real World Applications of Weighted Averages

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Summation Notation

Weighted Averages

Solving Problems with Technology

Summary

Applications

Summation Notation

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Before getting started, let's see the summation notation applied to averages.

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Weighted Averages

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Equation: Weighted average for n data:

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Here:

are the values.

are the weights of each value.

xi

Weighted averages are used to find an average when some values contribute more to the final average than others.

wi

And summations are:

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Calculating Final Grades

Example 1: In school, different assignments (homework, tests, projects) often have different weights. Let's suposse you obtained the grades as follows:

Final grade=2.7

Let's find out the final grade:

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Weights are the percentages of each assignment.

1. identify given values. n=3 x₁=4x₂=2x₃=3w₁=0.2w₂=0.5 w₃=0.3

2. Replace in the average formula.

3. Perform calculations.

Applications

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Investment Returns

Example 2: When calculating the return on a portfolio with different investments, the amount invested in each asset influences the overall return.

Return=7%

Table

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1. identify given values. n=2 x₁=0.05x₂=0.08w₁=1000w₂=2000

2. Replace in the average formula.

3. Perform calculations.

Solving Problems with Technology

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You can use spreadsheets to calculate weighted averages easily.

Spreadsheets include Excel or Google Sheets

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Using Google Sheets Manually:

Example 1: Let's calculate the final grade for the example 1, click on the spreadsheet below and follow the instructions.

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Check out the results clicking on "Answers" in the image.

1. From a computer, open gmail, then click on Sheets icon (Green):

2. Create a new Google sheets file:

3. Copy the content shown in the image of the right.

4. Multiply each cell of the column B with the cells of the column C: For example, write in another cell: =B2*C2 =B3*C3 =B4*C4

5.In front of "Total" sum the content of columns B and D: For Percentage: =SUM(B2:B4) For "Product": =SUM(D2:D4)

6. Divide the total of the column D over the the total of the column B. Paste in average cell: =D5/B5 This is the Final Grade.

Using a Google Sheets Formula:

Example 1: Let's calculate the final grade for the example 1 using the google sheet's formula AVERAGE.WEIGHTED()

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Check out the results clicking on "Answers" in the image.

1. From a computer, open gmail, then click on Sheets icon (Green):

2. Create a new Google sheets file:

3. Copy the content shown in the image of the right.

4. Next to to the Average cell, write the following formula: =AVERAGE.WEIGHTED(B2:B4,C2:C4) The formula automatically calculates the weighted average given the weights: B2:B4 and given the values:C2:C4

Summary:Calculating the Weighted Average

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Welcome 6th graders!

A journey soon begin through Social Science experiences!

Great job!

See you next time

9TH-REAL-WORLD-APPLICATIONS-OF-WEIGHTED-AVERAGES-EN © 2024 by CASURID is licensed under CC BY-NC-ND 4.0

MA.912.FL.1 Build mathematical foundations for financial literacy.MA.912.FL.1.3 Solve real-world problems involving weighted averages using spreadsheets and other technology.ELD.K12.ELL.MA.1 English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics.

Investment: Putting money into a business to buy new stock, machines, etc.,

Return: If a business or an investment returns an amount of money, it produces a profit, that is, additional money.

It is highly advised to have:

MATERIAL

• Grid paper.
• Pencils of different colors.
• Eraser.
• A rule.
• A calculator.
• Geogebra installed on your phone/tablet/computer (or use online version).

Whether it makes sense or no.

Check the Solution

Calculate products, then sum above and below fraction, finally divide both results.

Using the formula by hand or using the Excel/Google Sheets functions

Calculate the weighted average

Annotate/ underline/draw givens

In a paper or in spreadsheet

Identify the question and assign a letter for the unknown