Table of contents

1. Intro to Stats and Collecting Data1h 14m
2. Describing Data with Tables and Graphs1h 55m
3. Describing Data Numerically2h 5m
4. Probability2h 16m
5. Binomial Distribution & Discrete Random Variables3h 6m
6. Normal Distribution and Continuous Random Variables2h 11m
7. Sampling Distributions & Confidence Intervals: Mean3h 23m
8. Sampling Distributions & Confidence Intervals: Proportion1h 25m
9. Hypothesis Testing for One Sample3h 29m
10. Hypothesis Testing for Two Samples4h 50m
11. Correlation1h 6m
12. Regression1h 50m
13. Chi-Square Tests & Goodness of Fit1h 57m
14. ANOVA1h 57m

3. Describing Data Numerically

Mean

Statistics

3. Describing Data Numerically

Mean

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1:52 minutes

Problem 2.RE.16

Textbook Question

For the four test scores 96, 85, 91, and 86, the first 3 test scores are 20% of the final grade, and the last test score is 40% of the final grade. Find the weighted mean of the test scores.

Verified step by step guidance

Step 1: Understand the concept of a weighted mean. A weighted mean is calculated by multiplying each value by its respective weight, summing these products, and then dividing by the sum of the weights.

Step 2: Assign weights to each test score. The first three test scores (96, 85, 91) each have a weight of 20% (or 0.2), and the last test score (86) has a weight of 40% (or 0.4).

Step 3: Multiply each test score by its respective weight. For example, calculate 96 × 0.2, 85 × 0.2, 91 × 0.2, and 86 × 0.4.

Step 4: Add the weighted values obtained in Step 3. This gives the numerator of the weighted mean formula.

Step 5: Divide the sum from Step 4 by the total weight. The total weight is 0.2 + 0.2 + 0.2 + 0.4 = 1. This division gives the weighted mean of the test 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 an average that takes into account the relative importance or weight of each value in a dataset. In this case, different test scores contribute differently to the final grade based on their assigned weights. The formula for the weighted mean is the sum of each score multiplied by its weight, divided by the total of the weights.

Weights in Grading

Weights in grading refer to the proportionate influence that each component of a course has on the final grade. In this scenario, the first three test scores account for 20% each, while the last test score accounts for 40%. Understanding how these weights are distributed is crucial for calculating the overall performance accurately.

Calculation of Averages

Calculating averages involves summing a set of values and dividing by the number of values. For weighted averages, however, each value is multiplied by its respective weight before summing. This method ensures that more significant contributions to the average are appropriately represented, which is essential for accurately reflecting a student's performance based on varying test importance.

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Textbook Question

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Textbook Question

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Textbook Question

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Textbook Question

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