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Other Measures of Location

The sample median  is another popular measure of location besides the average. It is particularly useful for skewed distributions like household income, which have occasionally large outliers. Recall that the sample median is the middle value in an ordered array of the data, hence it is insensitive to extremely large observations. Consider the following data on household incomes:

    $40T, $50T, $55T, $65T, $65T, $145T
The average household income is $70T, so 5 out of the 6 households have lower than average income. The median household income is ($55T+$65T)/2=$60T, so half of the sample has income below median, and half have income above median. This is a useful property of the median that the average does not have: it separates the lower half of the data from the upper half. For instance, if your Exam 1 score is higher than the class median, then you know that you did better than at least half of the class. If your Exam 1 score is higher than the class average, it is still possible that your score belonged to the lower half of the class.


next up previous contents index
Next: Other Measures of Spread Up: Location and Spread Previous: The Variance

2003-09-08