Textbook Question
Building Basic Skills and Vocabulary
The length of a guest lecturer’s talk represents the third quartile for talks in a guest lecture series. Make an observation about the length of the talk.
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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 2.3.44
Finding a Weighted Mean In Exercises 41– 46, find the weighted mean of the data.
Credit Card Balance For the month of October, a credit card has a balance of \$115.63 for 12 days, \$637.19 for 6 days, \$1225.06 for 7 days, \$0 for 2 days, and \$34.88 for 4 days. What is the account’s mean daily balance for October?
Verified step by step guidance1
Step 1: Understand the concept of weighted mean. The weighted mean is calculated by multiplying each data value by its corresponding weight (frequency or duration), summing these products, and then dividing by the total weight (sum of frequencies).
Step 2: Identify the data values and their corresponding weights from the problem. The balances are \$115.63, \$637.19, \$1225.06, \$0, and \$34.88, and their respective durations are 12 days, 6 days, 7 days, 2 days, and 4 days.
Step 3: Multiply each balance by its corresponding duration to find the weighted contributions. For example, calculate \$115.63 × 12, \$637.19 × 6, \$1225.06 × 7, \$0 × 2, and \$34.88 × 4.
Step 4: Add all the weighted contributions together to find the total weighted sum. This represents the numerator of the weighted mean formula.
Step 5: Divide the total weighted sum by the total number of days (sum of all durations: 12 + 6 + 7 + 2 + 4) to calculate the weighted mean daily balance for October.
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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 or frequency of each value in a dataset. Unlike a simple mean, where all values contribute equally, the weighted mean assigns different weights to each value based on their significance. This is particularly useful in scenarios where certain data points are more relevant, such as calculating averages over varying time periods or quantities.
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Data Representation
Data representation involves organizing and summarizing data in a way that makes it easier to analyze and interpret. In the context of the credit card balance example, the data is represented by different balances over specific days. Understanding how to represent this data accurately is crucial for calculating the weighted mean, as it allows for clear identification of the values and their corresponding weights.
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Calculation of Weighted Mean
To calculate the weighted mean, you multiply each value by its corresponding weight, sum these products, and then divide by the total of the weights. In the credit card balance example, each balance is multiplied by the number of days it was held, and the total of these products is divided by the total number of days in October. This process ensures that the average reflects the influence of each balance based on the time it was maintained.
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Related Practice
Textbook Question
Determine whether the statement is true or false. If it is false, rewrite it as a true statement.
Class boundaries ensure that consecutive bars of a histogram touch.
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Textbook Question
Using Technology to Find Quartiles and Draw Graphs In Exercises 23–26, use technology to draw a box-and-whisker plot that represents the data set.
Hourly Earnings The hourly earnings (in dollars) of a sample of 21 employees at a consulting firm
25.89 27.09 31.76 28.28 26.19 27.43 24.06
25.61 22.56 29.76 18.01 23.66 38.24 37.27
32.70 31.12 25.87 15.06 23.12 30.62 19.85
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Textbook Question
Using and Interpreting Concepts
Finding and Discussing the Mean, Median, and Mode In Exercises 17–34, 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.
College Credits The number of credits being taken by a sample of 14 full-time college students for a semester
12 14 16 15 13 14 15
18 16 16 12 16 15 17
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Textbook Question
Using and Interpreting Concepts
Finding and Discussing the Mean, Median, and Mode In Exercises 17–34, 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.
Judicial System The responses of a sample of 34 young adult United Kingdom males in custodial sentences who were asked what is affected by such sentences (Adapted from User Voice)
Mental health: 8
Trust: 3
Education: 8
Personal development: 5
Family: 3
Future opportunities: 3
Other: 4
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Textbook Question
Building Basic Skills and Vocabulary
True or False? In Exercises 1–4, determine whether the statement is true or false. If it is false, rewrite it as a true statement.
A data set can have the same mean, median, and mode.
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