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12:15 - Progress saved Done \( \sqrt{0} \) Question 7 \( 0 / 5 \mathrm{pts} \) 100 Details What percentage of the general U.S. population have bachelor's degrees? The Statistical Abstract of the United States, 120th Edition, gives the percentage of bachelor's degrees by state. For convenience, the data are sorted in increasing order. \[ \begin{array}{c} 22,23,23,23,24,25,25,25,26,26,26,26,27,27,27, \\ 27,27,27,28,28,29,29,29,29,29,29,29,29,30,31, \\ 31,31,31,31,31,32,32,32,32,32,33,33,34,36,36, \\ 37,37,39,40,43 \end{array} \] In this method of identifying outliers, a data value is considered as an outlier if it is either above or below 2 standard deviations. Provided 29.76, 4.59 are mean value and standard deviation of this data set respectively. What are the outliers of this data set? 22, 43 \( 22,23,40,43 \) 22, 23 40, 43 39,40,43 Question Help: \( \triangle \) Message instructor Submit Question wamap.org

Ask by Kelley Hanson. in the United States
Jan 25,2025

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Answer

The outliers are 39, 40, and 43.

Solution

To determine the outliers in the given data set using the provided mean and standard deviation, follow these steps: 1. **Understand the Criteria for Outliers:** - A data point is considered an outlier if it is more than **2 standard deviations** away from the mean. 2. **Calculate the Thresholds:** - **Mean (\(\mu\))**: 29.76 - **Standard Deviation (\(\sigma\))**: 4.59 - **Lower Threshold**: \(\mu - 2\sigma = 29.76 - 2(4.59) = 29.76 - 9.18 = 20.58\) - **Upper Threshold**: \(\mu + 2\sigma = 29.76 + 2(4.59) = 29.76 + 9.18 = 38.94\) 3. **Identify Outliers:** - **Below 20.58**: There are no data points below 20.58. - **Above 38.94**: The data points **39, 40, 43** exceed 38.94. 4. **Conclusion:** - The outliers in the data set are **39, 40, and 43**. **Answer:** 39, 40, 43

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Did you know that the percentage of bachelor's degrees in the United States has grown significantly over the decades? In 1940, only about 4% of the U.S. population held a bachelor's degree! Fast forward to recent years, and that number is closer to 32%. This ongoing trend reflects educational reforms and the increasing value placed on higher education in the workforce. Identifying outliers in data sets can be quite the adventure! To find outliers, you'll calculate the range: anything below the mean minus 2 times the standard deviation and anything above the mean plus 2 times the standard deviation. For your data, anything below 20.58 (29.76 - 2*4.59) or above 38.94 (29.76 + 2*4.59) is considered an outlier. When you apply this rule, you'll find that the values 22 and 43 are the outliers in your set.

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