What is Mean, Median, and Mode?
Mean, median, and mode all represent averages. Now, typically when people think of finding the average they have the mean in mind. The mean is the one where you add up all the numbers, and divide by how many numbers there are. It’s true that is the most common kind of average, but, really, all three are a type of average.
Let’s take a look at how to find for each average.
First, the mean.
Let’s say we have a list of nine numbers:
23, 16, 54, 27, 31, 16, 33, 24, 19
So, to find the mean we need to add up all of the numbers in the list, then divide what we get by the amount of numbers in the list; which we know is nine.
When we add all the numbers up we get 243. So, now we take that number and divide it by 9 to get 27; and that’s all there is to finding the mean. Add up all the numbers on the list, then divide by how many numbers there are.
Finding the median is a little easier, because you don’t have to do any addition or division; which can get pretty crazy depending on how many numbers you have in your collection of data.
The median is literally the number in the “middle” of a list of numbers. However, before just looking at the number in the middle you must first arrange the set of numbers in ascending order, which means smallest to largest.
So, using our same list, if we arrange it in ascending order we get:
16,16,19,23,24,27,31,33, and 54.
We can see that the middle number is 24, and we know this because there are an equal amount of numbers on each side of 24. So, we have four numbers to the left, and four numbers to the right; putting 24 in the middle. Now, we can easily see the middle number in this list, because we only have nine numbers; but what happens when we have a list of one thousand numbers? I mean you can use the same method, but it may take you a little longer. So, mathematicians have graciously worked to give us a formula to make this process quicker. (n+1)/2. ‘N’ being the amount of numbers on the list. Now, let’s see if this works for us. Our ‘n’ is equal to nine, because there are nine numbers in the list. So, we have (9+1)/2, which is 10/2, which is 5. This five is telling us the the 5th number in the list is our median, which we can see, by looking back at our list, that this is true.
Finding the median, as you can see, is relatively simple… but it’s especially simple when we are looking for the median in a list with an odd amount of numbers. Like, in our case, we we have been working with a list of nine numbers. But what about when we have a list with an even amount of numbers…? Well, you still would use the same general method. You would set them up in ascending order, except now you take the mean of the two numbers in the middle.
So, let’s just add a number onto our list of nine. Let’s say 28. Now, we have:
16,16,19,23,24,27,28, 31,33, and 54.
Now, we take the mean of the fifth and sixth numbers. So we take the sum of 24 and 27, then divide by the amount of numbers that we are suming; which in this case is two. So, 24 + 27 is equal to 51. Then we divide by two, which gives us 25.5 as the median.
Okay, now onto mode.
Good news, the mode is definitely the simplest of the three to find. The mode is the number that appears the most amount of times. So, taking a look at our list that we have been using, we can see that there is only number that is repeated, and that is 16… and that is our mode. Simple enough. If there are no numbers that repeat, then there is no mode. Also, let’s pay close attention to our definition. The mode is the number that appears the most amount of times. So, it may be that you have a number repeat, but there is another number that repeats more. The number that repeats more is the mode… but you can have multiple modes. If two numbers are repeated the same amount of times, then they are both modes.
I hope this has been helpful.
For further help be sure to check out our other video’s here.
See you next time!