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If the sample has an odd number of items in it then the median will definitely be in the sample at least once because the median is value of the set of data items whose value(s) are in the middle of the sample when the sample is sorted from smallest to largest.
If the sample has an even number of items in it then if the middle items are different the median will be their average, and it will differ from all of the items in the data set.
I could continue in this vein but already you can see that the median sometimes occurs in a data set but not always.
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Measurement of qualitative variables using median?
The median shows where the 'middle' of your data is. For qualitative data, this only makes sense when the variable is ordinal. An ordinal variable is one whose values have a natural order, eg never/rarely/sometimes/often/always. If you have nominal data (qualitative data with no order) eg democratic/republican/other, you might find the mode (most common value) useful.
Since the median is the middle value of a data set it must always be?
Not an extreme value.
Does some quantitative data sets do not have a median?
No, they must have a median. However, if the data set is of even order, the median may not belong to the data set. For example, the median of 1,2,3,10 is halfway between 2 and 3 or 2.5 which is not a data point.
Which descriptive statistic always divides the data set such that 50 percent of the data values lie above it and 50 percent lie below it?
The median.
Should The mean or median be used in ordinal data?
The median is used when reporting ordinal data.
