Extending the Concepts Recall that in a symmetric distribution, the mean and median are approximately equal. In a skewed distribution, they are very different. Some students ask me how different the mean and median need to be to determine a distribution is skewed. For example, if the mean score on an exam is 86 and the median is 90, is this symmetric or skewed? The Pearson's Index of Skewness determines whether data is skewed. It is found by 3(X - Med) where s represents the standard deviation of the sample, X represents the mean, and Med represents the median. If the Pearson's Index is between -1 and 1 (inclusive), the data is considered roughly symmetric If PI is greater than 1, then the distribution is skewed right If PI is less than -1, then the distribution is skewed left 9. Consider a neighborhood where the mean home value is $302,000 and the median home value is $324,000. a. Based only on the mean and median, make a prediction: do you think this data is roughly symmetric or skewed? If it is skewed, what type of skewness (left or right) does this data have? b. If the standard deviation is $72,500, find the Pearson's Index. Show work using the formula =(X - Med) S .Then use the Pearson's index to determine the shape. Is it left skewed, right skewed, or roughly symmetric? c. Was your prediction correct? It's okay if the answer is no. d. Critical thinking question: why do you think the standard deviation is used in this calculation? Why is it helpful to consider standard deviation in determining skewness? Consider creating some examples of data sets of your own to help you understand. Answer in one to three complete sentences