Textbook Question
The overall averages of 12 students in a statistics class prior to taking the final exam are listed.
67 72 88 73 99 85 81 87 63 94 68 87
d. Display the data in a stem-and-leaf plot. Use one line per stem.
Ch. 2 - Descriptive Statistics
Larson8th EditionElementary Statistics: Picturing the WorldISBN: 9780137493470
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Table of contents
- Ch. 1 - Introduction to Statistics87
- Ch. 2 - Descriptive Statistics176
- Ch. 3 - Probability184
- Ch. 4 - Discrete Probability Distributions102
- Ch. 5 - Normal Probability Distributions183
- Ch. 6 - Confidence Intervals154
- Ch. 7 - Hypothesis Testing with One Sample165
- Ch. 8 - Hypothesis Testing with Two Samples134
- Ch. 9 - Correlation and Regression87
- Ch. 10 - Chi-Square Tests and the F-Distribution87
Larson8th EditionElementary Statistics: Picturing the WorldISBN: 9780137493470Not the one you use?Change textbook
Chapter 2, Problem 2.RE.16
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.
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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.
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Calculating the Mean
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.
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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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Related Practice
Textbook Question
In Exercises 5 and 6, use the data set, which represents the number of rooms reserved during one night’s business at a sample of hotels.
153 104 118 166 89 104 100 79 93 96 116
94 140 84 81 96 108 111 87 126 101 111
122 108 126 93 108 87 103 95 129 93 124
Construct a frequency distribution for the data set with six classes and draw a frequency polygon.
Textbook Question
In Exercises 37– 40, use the data set, which represents the model 2020 vehicles with the highest fuel economies (in miles per gallon) in the most popular classes. (Source: U.S. Environmental Protection Agency)
36 30 30 45 31 113 113 33 33 33 52 141 56 117 58
118 50 26 23 23 27 48 22 22 22 121 41 105 35 35
About how many vehicles fall on or below the third quartile?
Textbook Question
In Exercises 13 and 14, find the mean, the median, and the mode of the data, if possible. If any measure cannot be found or does not represent the center of the data, explain why.
The responses of 1019 adults who were asked how much money they think they will spend on Christmas gifts in a recent year (Adapted from Gallup)
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Textbook Question
According to data from the city of Toronto, Ontario, Canada, there were nearly 112,000 parking infractions in the city for December 2020, with fines totaling over 5,500,000 Canadian dollars. The fines (in Canadian dollars) for a random sample of 105 parking infractions in Toronto, Ontario, Canada, for December 2020 are listed below. (Source: City of Toronto)
In Exercises 1–5, use technology. If possible, print your results.
Find the sample mean of the data.
Textbook Question
In Exercises 1 and 2, use the data set, which represents the overall average class sizes for 20 national universities. (Adapted from Public University Honors)
37 34 42 44 39 40 41 51 49 31
52 26 31 40 30 27 36 43 48 35
Construct a relative frequency histogram using the frequency distribution in Exercise 1. Then determine which class has the greatest relative frequency and which has the least relative frequency.
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