A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN: 9780134753119
Author: Sheldon Ross
Publisher: PEARSON
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Question
### Understanding Positively Skewed Distributions A positively skewed distribution occurs when the data values tend to gather around the lower end of the scale, with the longer tail extending towards the higher end. When interpreting dot plots for such distributions, understanding the characteristics of their tails is crucial. Consider the following question regarding positively skewed distributions: **Question:** A distribution is positively skewed if which of these statements is true about the dot plot that represents it? - **A.** The right tail is longer than the left. - **B.** The left tail is equal in length to the right tail. - **C.** The left tail is longer than the right. - **D.** The left side is a mirror reflection of the right side. **Correct Answer:** - **A.** The right tail is longer than the left. ### Explanation: In a positively skewed distribution, where more lower values are clustered, the data's "tail" on the right side (higher values) is longer. This indicates that while most data points fall within the lower ranges, a few exceptionally high values stretch out the tail on the right side. Hence, for a positively skewed dot plot, look for a longer right tail.
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Transcribed Image Text:### Understanding Positively Skewed Distributions A positively skewed distribution occurs when the data values tend to gather around the lower end of the scale, with the longer tail extending towards the higher end. When interpreting dot plots for such distributions, understanding the characteristics of their tails is crucial. Consider the following question regarding positively skewed distributions: **Question:** A distribution is positively skewed if which of these statements is true about the dot plot that represents it? - **A.** The right tail is longer than the left. - **B.** The left tail is equal in length to the right tail. - **C.** The left tail is longer than the right. - **D.** The left side is a mirror reflection of the right side. **Correct Answer:** - **A.** The right tail is longer than the left. ### Explanation: In a positively skewed distribution, where more lower values are clustered, the data's "tail" on the right side (higher values) is longer. This indicates that while most data points fall within the lower ranges, a few exceptionally high values stretch out the tail on the right side. Hence, for a positively skewed dot plot, look for a longer right tail.
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