Table of contents

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 53m
8. Sampling Distributions & Confidence Intervals: Proportion1h 12m
- Sampling Distribution of Sample Proportion
  29m
- Confidence Intervals for Population Proportion
  42m
9. Hypothesis Testing for One Sample2h 19m
10. Hypothesis Testing for Two Samples3h 22m
11. Correlation1h 6m
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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2:52 minutes

Problem 2.3.44

Textbook Question

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 guidance

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.

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.

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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Textbook Question

Extending Concepts

Trimmed Mean To find the 10% trimmed mean of a data set, order the data, delete the lowest 10% of the entries and the highest 10% of the entries, and find the mean of the remaining entries.

a. Find the 10% trimmed mean for the data in Exercise 65.

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Textbook Question

Extending Concepts

Trimmed Mean To find the 10% trimmed mean of a data set, order the data, delete the lowest 10% of the entries and the highest 10% of the entries, and find the mean of the remaining entries.

c. What is the benefit of using a trimmed mean versus using a mean found using all data entries? Explain your reasoning.

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Textbook Question

In Exercises 37– 40, without performing any calculations, determine which measure of central tendency best represents the graphed data. Explain your reasoning.

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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?

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Textbook Question

Which statistic is the best unbiased estimator for μ?

a. s

b. xbar

c. the median

d. the mode

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