if the data set contains an odd number of items

Question

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)/2^th  item gives the median and when the total of the frequencies is even, say, 2n, then n^th 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.