## Median for ungrouped data, Applied Statistics

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If the data set contains an odd number of items, the middle item of the array is the median. If there is an even number of items, the median is the average of the two items. If the total of the frequencies is odd, say n, the value of the (n+1)/2th  item gives the median and when the total of the frequencies is even, say, 2n, then nth and (n + 1)th are two central items and the arithmetic mean of these two items gives the median.

### Example

The following data relates to the sales figures of certain companies relating to the year 2000-2001:

 Companies Sales ACC 1520 Andhra Valley 436 Excel Inds 228 Indian Hotels 239 Tata Hydro 292 Tata Power 734 Tata Tea 412 Voltas 980 Tomco 312 Tinplate Co. 256

The median for the above data can be obtained as follows:

The series should first be arranged in an appropriate order. In the present case it is in descending order.

 Company Sales Rank ACC 1520 1 Voltas 980 2 Tata Power 734 3 Andhra Valley 436 4 Tata Tea 412 5 Tomco 312 6 Tata Hydro 292 7 Tinplate Co. 256 8 Indian Hotels 239 9 Excel Inds 228 10

Now, median is the mean of the 5th and the 6th items, i.e.  (412 + 312)/2 = 362.

Thus, the median sales value of the ten companies is 362.

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