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Role of Standard Deviation in the Descriptive Statistic

Weather reports typically report the daily high and low temperatures, the average temperature for the day, and the record low and high temperatures for a given day. Given that today's high is 70, the average high for this date is 60, the record low for this date is 30, and the record high for this date is 85, what additional information (i.e., descriptive statistic(s) would you like to have in order to determine if the 70-degree temperature is a significant departure from the average temperature for that date of the year in that particular location? Other variables such as humidity, other locations, other days of the year, etc. will not be considered.

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Ans: for descriptive statistic, we usually need to know the mean and standard deviation. In our case, since the average high for this date is known (60), the additional information ...

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The solution gives detailed discussion on the role of standard deviation in the descriptive statistic with a worked example.