Carl Horowitz

**University of Michigan**

Runs his own tutoring company

Carl taught upper-level math in several schools and currently runs his own tutoring company. He bets that no one can beat his love for intensive outdoor activities!

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There are different methods we use for analyzing data. Some of the most common ways that we analyze data is to identify the mean, median and mode of a set of numbers. When **analyzing data** we are sometimes asked to use a box and whisker plot, or to find the percentiles of a list of numbers. These methods for analyzing data deal are used for real numbers and can be decimals, integers, or another classification of the real numbers.

One of the main applications of Math is using it to analyze data and in order to analyze data we actually have some terms that we frequently refer to, okay? So what I have is a pretty straight forward simple set of data, we just have a couple of numbers up here and we're going to try to find the mean, median and mode.

Mean is just a fancy way of saying average. So to find the average all we do is add everything up and we divide by the number of terms, okay? So to add everything up. Here we have 10 here we have 10 so that adds up to 20 and we add in 8 so we add up to 28 and we have 1, 2, 3, 4, 5, 6 terms, so mean is just going to be 28 over 6. Okay.

Our median is basically just the middle of data, okay? So in order to make this work what we have to do is arrange our data from smallest to greatest or greatest to smallest or basically either completely ascending or descending. This case everything is going up so we have it in ascending order, and we're just trying to find the middle term. Okay? So there are six terms which means we don't really have a term directly in the middle, so what we do is we average the two terms on either side of it okay? So we count it up three, we count it down three. These are sort of our two middle terms, so the median is just going to be the average of those two terms. 4+5 is 9, 9 divide by 2 is just going to be 4 and a half. Okay? So if you have a even number of terms your median is just going to be the average of the two middle terms. If you have an odd number of terms, say I threw in a two right here, then I would have a median a middle term completely. Okay then this four would be my middle term because I would have three on the other side.

Okay. The last thing that we refer to is called the mode which is just going to be the number that occurs the most frequently, okay? So 3 occurs once, 4 occurs twice, 5 occurs twice, 7 occurs once. So in this case I actually have two modes. I have both 4 and 5, okay? If they were just one say this four wasn't here then I would have two 5's and one of everything else, then my mode would be 5, it's the number that occurs most frequently. Okay?

So just some language that comes up frequently when we're analyzing data is mean, median and mode.