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I was working through problems of the median (grouped data). I encountered a problem where the classes were not continuous, and my textbook said that I needed to make them continuous since the median formula assumes continuity.

If the classes were not continuous, the median wouldn't change by much, right? So why does the median formula work under the assumption of continuity -- what happens if the classes are not continuous?

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  • $\begingroup$ What do you mean by continuous? Integers are real numbers and the median here is perfectly fine, or did you mean that your variables are categorical? $\endgroup$ Oct 12, 2018 at 6:09

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The median is a measure of central tendency and is the most common value in a range of values (continuous). If you have a variable where the only possible values are 0 and 1 (dichotomous; e.g. male or female) you can also find the more common value but this would be less meaningful than the proportion of cases in your data with each value (%54 male vs %46 female, for example).

However, if you have a range of values and would like to get a sense of the most common value then the median is meaningful. The mean (average) may be meaningful as well unless you have a variable with a skewed range of values. A good example of this is house prices, the mean may be pulled up toward really wealthy homes and therefore the median may be more descriptive of the actual center of the distribution of house prices.

https://en.wikipedia.org/wiki/Central_tendency

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