[Verified] A Teacher Surveys A Random Group Of Students About Their Preference For Doing Classwork Online Or On Paper. The Results Are Shown In The Table Below.

A Teacher Surveys A Random Group Of Students About Their Preference For Doing Classwork Online Or On Paper. The Results Are Shown In The Table Below.

Student Classwork

Preference

PreferenceNumber of Students
Paper17
Online8

Based on the results, how many students out of 350 will most likely have a preference to do their class work online?

To determine how many students out of 350 will most likely have a preference to do their classwork online based on the survey results, we can use the concept of proportions.

Concept Used: Proportions

A proportion is a relationship between two ratios. In this case, we’ll use the ratio of students who prefer online classwork from the survey to predict the number out of 350 students.

Step-by-Step Calculation:

1. Determine the Ratio of Students Who Prefer Online Classwork

Given from the survey: Number of students who prefer paper = 17 Number of students who prefer online = 8

Total students surveyed = 17+8=2517+8=25

Ratio of students who prefer online = 825258​

2. Use the Ratio to Predict the Number Out of 350 Students

Using the proportion: Number who prefer online from surveyTotal surveyed=Number who would prefer online out of 350350Total surveyedNumber who prefer online from survey​=350Number who would prefer online out of 350​

Given: 825=�350258​=350x

Where �x is the number of students out of 350 who would most likely prefer online classwork.

To solve for �x, we can cross-multiply:

8×350=25×�8×350=25×x

Let’s solve for �x to get the predicted number of students out of 350 who would prefer online classwork.

2. Use the Ratio to Predict the Number Out of 350 Students (Continued)

From the calculation: 8×350=25×�8×350=25×x �=112x=112

Therefore, based on the survey results, it is predicted that 112 students out of 350 will most likely have a preference to do their classwork online.

Conclusion: Out of 350 students, 112 will most likely prefer to do their classwork online.

more intuitive and quicker way to approach this problem using the concept of scaling.

Let’s delve deeper into the shortcut method.

Scaling Using Percentages

Concept Used: Percentage Scaling

Percentage scaling is a method where we determine the percentage representation of a part relative to the whole and then use that percentage to predict or scale to a different total.

Detailed Explanation:

1. Determine the Percentage of Students Who Prefer Online Classwork

To find out the percentage of students who prefer online classwork based on the survey:

  • First, we determine the fraction of students who prefer online classwork. This is given by: Fraction of students who prefer online=Number of students who prefer onlineTotal students surveyedFraction of students who prefer online=Total students surveyedNumber of students who prefer online​

Given: Number of students who prefer online = 8 Total students surveyed = 25

Fraction=825Fraction=258​

  • Next, to convert this fraction into a percentage, we multiply by 100: Percentage who prefer online=825×100%Percentage who prefer online=258​×100%

This gives us the percentage of students from the survey who prefer online classwork.

2. Apply the Percentage to the 350 Students

Once we have the percentage of students who prefer online classwork:

  • We can use this percentage to predict the number of students out of any total number who would have the same preference. In this case, we want to predict for 350 students.

Number of students out of 350 who prefer online=Percentage who prefer online100×350Number of students out of 350 who prefer online=100Percentage who prefer online​×350

This formula scales the known percentage to a new total, allowing us to predict the number of students out of 350 who would prefer online based on the survey results.

Conclusion:

Using percentage scaling, we can easily and quickly predict outcomes for different totals based on known proportions or percentages. In this case, we determined that 32% of students from the survey prefer online classwork. When we scale this percentage to a total of 350 students, we predict that 112 students will have the same preference. This method is efficient because it directly applies the known proportion (in the form of a percentage) to a new total.

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