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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2:07 minutes

Problem 2.3.66c

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.

Verified step by step guidance

Step 1: Understand the concept of a trimmed mean. A trimmed mean is a measure of central tendency that removes a specified percentage of the smallest and largest data points before calculating the mean. This helps reduce the influence of outliers.

Step 2: The benefit of using a trimmed mean is that it provides a more robust measure of central tendency, especially when the data set contains extreme values (outliers) that could skew the mean calculated using all data entries.

Step 3: By removing the lowest 10% and highest 10% of the data, the trimmed mean focuses on the central portion of the data, which is often more representative of the typical values in the data set.

Step 4: Using a trimmed mean can improve the accuracy of statistical analysis in cases where the data distribution is not symmetric or contains anomalies, as it reduces the impact of extreme values.

Step 5: In summary, the trimmed mean is beneficial because it provides a more reliable and less sensitive measure of central tendency in the presence of outliers or non-normal data distributions.

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Key Concepts

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

Trimmed Mean

A trimmed mean is a statistical measure that involves removing a specified percentage of the lowest and highest values from a data set before calculating the mean. This approach helps to reduce the influence of outliers or extreme values, providing a more robust central tendency measure that better represents the majority of the data.

Outliers

Outliers are data points that significantly differ from other observations in a data set. They can skew the results of statistical analyses, particularly measures like the mean, leading to misleading conclusions. By using a trimmed mean, the impact of these outliers is minimized, resulting in a more accurate reflection of the data's overall trend.

Robust Statistics

Robust statistics are methods that provide reliable results even when assumptions about the data are violated, such as the presence of outliers. The trimmed mean is an example of a robust statistic, as it focuses on the central portion of the data, making it less sensitive to extreme values and thus offering a more stable measure of central tendency.

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Textbook Question

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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.

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.

b. Compare the four measures of central tendency, including the midrange.

Textbook Question

Finding a Weighted Mean In Exercises 41– 46, find the weighted mean of the data.

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Textbook Question

Finding a Weighted Mean In Exercises 41– 46, find the weighted mean of the data.

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Multiple Choice

Find the mean of the sample data below.

Textbook Question

Geometric Mean The geometric mean is often used in business and economics for finding average rates of change, average rates of growth, or average ratios. To find the geometric mean of n values (all of which are positive), first multiply the values, then find the nth root of the product. For a 6-year period, money deposited in annual certificates of deposit had annual interest rates of 0.58%, 0.29%, 0.13%, 0.14%, 0.15%, and 0.19%. Identify the single percentage growth rate that is the same as the six consecutive growth rates by computing the geometric mean of 1.0058, 1.0029, 1.0013, 1.0014, 1.0015, and 1.0019.

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