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 3m
- 8. Sampling Distributions & Confidence Intervals: Proportion1h 12m
- 9. Hypothesis Testing for One Sample1h 1m
- 10. Hypothesis Testing for Two Samples2h 8m
- 11. Correlation48m
- 12. Regression1h 4m
- 13. Chi-Square Tests & Goodness of Fit1h 20m
- 14. ANOVA1h 0m
3. Describing Data Numerically
Mean
Problem 2.3.66b
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.

1
Order the data set in ascending order. This step ensures that the data is properly arranged for identifying the lowest and highest 10% of the entries.
Determine the number of entries to trim from both ends of the data set. Multiply the total number of data points by 10% (0.10) to find how many values to remove from the lowest and highest ends. If the result is not an integer, round to the nearest whole number.
Remove the lowest 10% and the highest 10% of the data points based on the calculation from the previous step. This leaves the middle portion of the data set.
Calculate the mean of the remaining data points. Add up all the remaining values and divide by the number of remaining data points to find the trimmed mean.
Compare the trimmed mean with the other measures of central tendency: the mean (average of all data points), the median (middle value of the ordered data set), and the midrange (average of the smallest and largest values in the data set). Discuss how the trimmed mean differs and why it might be more robust in the presence of outliers.

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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Trimmed Mean
The trimmed mean is a statistical measure that reduces the influence of outliers by removing a specified percentage of the lowest and highest values from a data set before calculating the mean. For example, in a 10% trimmed mean, the lowest 10% and highest 10% of data points are discarded, allowing for a more robust average that better represents the central tendency of the remaining data.
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Measures of Central Tendency
Measures of central tendency are statistical metrics that summarize a set of data by identifying the center point or typical value. The most common measures include the mean (average), median (middle value), mode (most frequent value), and midrange (average of the highest and lowest values). Each measure provides different insights, especially in the presence of skewed data or outliers.
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Midrange
The midrange is a simple measure of central tendency calculated by taking the average of the maximum and minimum values in a data set. It is defined as (max + min) / 2. While easy to compute, the midrange can be heavily influenced by outliers, making it less reliable than other measures like the mean or median in skewed distributions.
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