Why is the Median a thing? Why would someone need to find the Median of a data set?

Question

I know it’s a common saying that statistics isn’t intuitive to humans. I’ve read my Taleb. *Intuitively*, I can see why one might need to find the mean (average) of a data set as well as the mode.

But where and why would someone need to find the Median? I’ve never calculated the median of a data set in daily life. On the other hand, I compute the mean of several values multiple times a week sometimes. I don’t calculate Modes that much, but I can see **why** someone would care about the most-occurring value.

Can someone explain the relevance of finding the Median? I’m sure there are plenty of useful applications and I’m just unaware of them.

Thanks in advance!

In: 4

Answer 1

I am a microscopist and part of my analysis involves looking at “blinking” molecules, where if you’re looking in a microscope the pixels are dark most of the time but sometimes they are bright and on. As part of processing the image we like to subtract the “background” of the image, the part of the image that is visibile the whole time, from each frame. Picture a video of an immobile cell, where sometimes molecules randomly blink “on” and you get occasional bright spots. If you take every frame of the video and subtract off the cell, what you get is a video of just the blinking, making it easier to analyze them.

For each pixel, we *could* subtract off the average brightness of the pixel over the whole video. However, the bright spots will affect the average. If the pixel value is ~10 most of the time but sometimes it goes up to 200, then its average value will be higher than surrounding pixels without blinking molecules. This may be ok, but it means when you subtract off the average of the background, the blinking will not be as distinct.

Instead, if we subtract off the *median* pixel intensity, for the same movie the background median is going to be ~10, because the very high pixel intensities are outliers and their values aren’t incorporated into calculating the median.

This is just an example, but for general measurements where you want to characterize the “center” of the data but you don’t want very large or small outliers to affect that measurement, the median is generally your first choice.