Finding a Weighted Mean In Exercises 41– 46, find the weighted me...

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1. Intro to Stats and Collecting Data55m
2. Describing Data with Tables and Graphs1h 55m
3. Describing Data Numerically1h 45m
4. Probability2h 16m
5. Binomial Distribution & Discrete Random Variables2h 33m
6. Normal Distribution and Continuous Random Variables1h 38m
7. Sampling Distributions & Confidence Intervals: Mean1h 3m
- Introduction to Confidence Intervals
  15m
- Confidence Intervals for Population Mean
  48m
8. Sampling Distributions & Confidence Intervals: Proportion1h 12m
- Sampling Distribution of Sample Proportion
  29m
- Confidence Intervals for Population Proportion
  42m
9. Hypothesis Testing for One Sample1h 1m
- Steps in Hypothesis Testing
  1h 1m
10. Hypothesis Testing for Two Samples2h 8m
11. Correlation48m
- Scatterplots & Intro to Correlation
  26m
- Correlation Coefficient
  21m
12. Regression1h 4m
13. Chi-Square Tests & Goodness of Fit1h 20m
14. ANOVA1h 0m

3. Describing Data Numerically

Mean

Statistics

3. Describing Data Numerically

Mean

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1:53 minutes

Problem 2.3.41

Textbook Question

Finding a Weighted Mean In Exercises 41– 46, find the weighted mean of the data.
Final Grade The scores and their percents of the final grade for a statistics student are shown below. What is the student’s mean score?

Verified step by step guidance

Step 1: Understand the concept of weighted mean. The weighted mean is calculated by multiplying each score by its corresponding weight (percentage of the final grade), summing these products, and then dividing by the total weight (which should sum to 100%).

Step 2: Convert the percentages into decimal form for easier calculations. For example, 5% becomes 0.05, 35% becomes 0.35, and so on.

Step 3: Multiply each score by its corresponding weight in decimal form. For example, for Homework: 85 × 0.05, for Quizzes: 80 × 0.35, for Project/Speech: 100 × 0.35, and for Final Exam: 93 × 0.25.

Step 4: Add all the weighted scores together. This sum represents the numerator of the weighted mean formula.

Step 5: Divide the sum of the weighted scores by the total weight (which is 1, since all percentages add up to 100%). This will give the weighted mean of the student's scores.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Weighted Mean

The weighted mean is a type of average that takes into account the relative importance of each value. Unlike a simple average, where all values contribute equally, the weighted mean assigns different weights to each value based on their significance, often represented as percentages. This is particularly useful in scenarios like calculating final grades, where different assessments contribute differently to the overall score.

Percentages

Percentages represent a fraction of 100 and are used to express how a part relates to a whole. In the context of the weighted mean, percentages indicate the weight or importance of each score in the overall calculation. Understanding how to convert these percentages into decimal form is crucial for accurately computing the weighted mean.

Calculation of Weighted Mean

To calculate the weighted mean, multiply each score by its corresponding weight (percentage), sum these products, and then divide by the total of the weights. This process ensures that each score contributes to the final mean in proportion to its significance, allowing for a more accurate representation of the student's overall performance based on the different assessments.

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Finding a Weighted Mean In Exercises 41– 46, find the weighted mean of the data.Final Grade The scores and their percents of the final grade for a statistics student are shown below. What is the student’s mean score?