Measures of Central Tendency - Median

(Intro IVR: 16 sec)

Next coming to the median.

Median, like its name suggests, it is the exact middle value in any distribution when, we are arranging any distribution in ascending or descending order.

The important thing about median is that you will have to first sort your data, you can do it in ascending or descending order, that doesn't make a difference.

But data should be sorted, and its middle value will give you the median value.

So, basically what median does is it divides our distribution in half.

So, 50% of the observations will be on the right side of the median, and another 50% of the observations would be on the left side of the median.

Now the observations can also be even, and they can also be odd.

So, suppose if I have an odd number of observations with me, okay.

And you have sorted them.

Suppose, if I have this particular distribution, in which there are 11 members, and let's consider that, this is the retirement age distribution that I have got of the 11 people.

If you see in this particular data, we have arranged them into ascending order.

So, there are 11 distributions, this means that I want its 50^th ratio, I want its 50^th percentile.

So, what will I do? The 6th value which is right in the middle.

If you see the sixth value, which is 57.

Five values before the distribution which is on the left and there are five values after is the distribution which is on the right.

So, 57 is the exact number which is dividing my entire distribution into half and it is giving me an exact value.

Now, if my distribution is even, even means that suppose, in the same distribution let's consider that one more value comes.

And now I have 12 values in a particular data set.

I cannot divide it in half.

What will happen in that particular scenario? I will take the mean of the middle two values.

One particular value that will come, that single value would be my median.

Suppose in this situation I took a mean of 56 and 57 which is divided by 2, 56.5 is the particular value that I got, that would be called the median.

Like we had seen, the order doesn't affect it.

You can arrange it in ascending order or in descending order.

Centre value will always remain the same.

Let's see It's advantages of the median.

This doesn't get affected by extreme values.

Basically, they are not getting affected by outliers.

Now, suppose in my data set there is any extreme value, they can be smaller values or extremely larger values.

The median doesn't consider them because it takes only the centre value.

So, this becomes an advantage, as the outliers are not affecting it, usually, median is the preferred measure of central tendency when the distribution is not symmetrical, or when we have skewed data, we may use medium at that time.

It basically converts all the disadvantages of mean into advantage, which is during outliers and skewed data, mean used to not function and in that particular scenario we can use median.

Let's also see the disadvantages of median.

Since it doesn't use all the values, it just takes the centre value and gives us a particular figure So, basically it doesn't use our entire information.

Second is, it is the same thing, because you're playing with the numbers so you cannot use median for the categorical data.

So, we are not using median and mean for categorical data.

We just use it for numerical data.

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 (outro: 15 sec)