Well, wait a minute and read carefully! This article is NOT about explaining the summary measure formulae.
No, you have a million other articles for that and you have seen that all for a million times. Then, why read this? Well, I am trying to make a bit of sense out of the same old same old central tendency measures. One prerequisite, therefore, browse my site or YouTube and learn the summary measure basics. Because, without those basics, this article will be Mean for you!
Okay, so let us consider the Mean. Mean is the one single value using which you could represent a whole series of data. Simple, that is the practical meaning of the mean. If in your town, the last five days had the following temperatures in Fahrenheit; say, 65,60,70,75,65, and your friend asks you, "What was the temperature like last few days?", you won't be a robot to feed your friend with all five days' temperatures. You would simply say, well, it was around 67 degrees. How did you know it was 67 degrees; you knew it thanks to the mean. Add all five temperatures, divide by five, and BAM! you have a magic number to represent them all.
So what's the median then? Median serves a specific purpose. The median is the data point, which cuts your data set in half. Nothing more, nothing less. To get your median, you have to have your data set in ascending or descending order. Our data set above will be 60 60,65,65,70,75 in ascending order. The midpoint is the 3rd data point (you simply add 1 to the number of data points and divide by 2), and that data point is the 3rd data point, which is 65. A lot of fellows know how to calculate the median, but they do not know how to use it. Like I said earlier it cuts the data set into two. So what? Well, now you have two subsets where one has lower values and the other has higher values. So now you can investigate the two subsets differently to gauge further.
The Mode is simple. What data point appears most of the time? In our data set above, the mode is 65, which appears two times. When there are two modes, we call the data set a bi-modal data set, and when there are many modes, we call it a multi-modal data set. When there's no mode, do not invent anything, just say the mode is non-existent.
If you ask me which summary measure is the best, it is like you asking your mom which of her kids is the best (given she has more than one kid). The study of summary measures is not to find the best measure or a statistical panadol. Your best measure depends on your data set. A stable, continuous data set would need an analysis based on the mean, and a more erratic, sporadic data set with extreme values would need an analysis based on the median. Your best measure simply depends on the data set at hand and what you want to do with it.
