When a set of raw data is listed in order of size, the value which pitches up precisely in the middle of the arrangement is called the median.
When you have an odd number of values, there will be one number which lies precisely in the center. This will be the median.
But bear in mind, if there are an even number of results, the median will lie halfway between the two results which are in the middle.
Let us address an example of both to explain this point.
437 51 908 886 393 54 603 888 443 189 348
We are given a set of data which is in no obvious progression. This is known as raw data. The first thing to do is to organize the raw data in order of size. This must be done carefully, erasing the numbers as you enter them in your new list. Thus, you will never miss any numbers in between the stages.
51 54 189 348 393 437 443 603 886 888 908
After you have achieved this, count the number of values in the list.
You should find that there are eleven. But which of these will be the middle value?
If you leave out the value which occurs exactly in the center, there will be 10 results left behind. Half of ten is five, and for that reason the sixth number has to be the median. It is quite easy if you think about it.
The sixth value in the ordered list is 437, and thus this is the median of the given series of data.
Let’s check out the system for an even number of results.
First off, line up the values in ascending order of magnitude and count the number of values.
If for example, we discover there are 10, there isn’t one value which is positioned precisely in the center, but two.
Well, first of all, divide ten by two. This tells us that the fifth number has to occur at the end of the first half of the values and so the sixth number must come at the beginning of the second half of the values.
92 183 248 333 628 641 792 888 908 999
We look along the list and find that the fifth value is 628 and the 6th result is 641. To identify the median lying halfway between the values, we simply add the 5th and 6th values together before dividing by 2.
It is important to recognize that whenever there are an even number of observations, the median is not inevitably one of the given numbers.
Can you think of an occurrence where the median of an even number of observations is one of the given values? This can only be the case when the 2 numbers in the center are exactly the same, for example 80 and 80, where the median would be 80.
When given raw data, it is quite simple to uncover the median in this way.
