Okay. Now, we’re going to talk about mean, median, mode and range. So the problem tells us to find the mean, median, mode and range of each data set.
So here we have our data set. It’s a table and we see that. It says, the football league career touchdowns. So it had each player, player a, b, c and d, and then their respective career touchdowns. So let’s first start with our mean.
So the mean is the sum of all your items divided by the number of items in a set. So your mean is the sum of all your items divided by your total number of items in your set. So if we want to find the mean, we need to use this formula. So to find our mean, we need to first find the sum of our items. Well, here are our items and we need to add them up to find the sum. So I’m going to take 420 + 300 + 220 + 220. So that’s our first step. Once we’re done adding this up, we then have to divide it by to the total number of items in the set. So our total number of items in the set will be 4. So we have four items.
So our second step now is to add this up—to sum up all these items. So if I add 420 + 300 + 220 + 220, I get 1,160, and then I have to divide that by 4. If I take 1,160/4, I get 290. So our mean then is 290 touchdowns. Because in our table, we are talking about football league career touchdowns, our answer is going to be in touchdowns.
Let’s move on to the median. So your median is basically your central value or that middle value when the data are in ascending order. So remember that ascending order is from least to greatest. So 1 2 3 4, that’s an ascending order. So our median is the central value. I like to think median as middle value or central value, so it’s that middle number when your data is an ascending order. So our first step in finding our median is that we need to put it in an ascending order. Ascending is from least to greatest. I’m going to start with my least number and I have two which are the same which is fine. So I’m going to take 220 and 220 again because I have two and I have to include all of the numbers. So 220 and then 300 and then 420.
So now, I need to find that central value or that middle number. So I’m going to work from the two outside and then I’m going to go in and I noticed that I have two middle numbers because I have an even set. Anytime that you have an even set of numbers, you’re going to get two middle numbers. When that happens, you now have to find the mean of these. And remember, the mean is also called the average. So when you’re doing your mean, it’s finding the average. So I’m going to find the average of these numbers to get my median. So remember, to find the mean or to find the average, we have to sum up all our items and divide it by the total number of items in the set. So, I’m going to sum up my items while I have 220 and 300, so those are my two central values, my two middle values. So I’m going to take 220 + 300 and then after I sum up all my items, I divide it by the total number of items in the set, so I have two items. So 220 + 300 is 520/2, and that gives me 260. So my mean, my average is 260 so my median is now 260 touchdowns.
So let’s move on now to mode. Alright, I’m going to move over here for a little bit more room. So the mode is pretty simple. The mode is the value or values that occur most often. So in our set of data that we’re looking here, I have 420, 300, 220 and 220. So the value that I see that occurs the most often is 220. Sometimes as a side note, if you have a lot of numbers in your data set, if you’ve already found your median and you’ve already put them in ascending order, it might be helpful to look at them in order and see if there’s any numbers repeated. So we only have four values today so we can just—it’s pretty easy to look.
So I see that the only number that is repeated is 220. So our mode is 220 touchdowns. Sometimes, you may find that you have a set of data and you might have more than one value that is repeated the same time. You might have—for instance, if we had 420, 420, 300. 220, 220. So we have two numbers or two values that occur in an equal number of time. When that happens, the data set has no mode. So it’s something just to keep in mind. But here, 220 is repeated the most often so that’s our mode, so 220 touchdowns.
The last part of our problem is range. So the range is the difference between the greatest value in your data set and it’s the difference. So to find the range, it’s the greatest value minus the least value. So we take our greatest minus the least. So I’m looking at the difference. So the greatest value in our data set is 420. Again, it could also be happening in an ascending order. Just look to your right, 420. So 420 – 220. So if I were to subtract these, 420 – 220, it’s 200. So our range is 200 touchdowns.
So really quick to wrap up, our mean is also known as the average. So when you’re finding the mean, you’re also finding the average and vice versa. So to find the mean, it’s the sum of all your items divided by your total number of items in the set. To find your median, first, you put your data in ascending order from least to greatest and then you find your middle number, your central value or your middle value. If you have an even number in your data set, then you have to find the mean or the average of those two middle values, those two central values. And then once you find your average of those two, that is your median. And the mode is the value or values that occur most often. And remember that if all the values occur in equal number of times, the data set has no mode. And lastly, the range, the range is your difference between your greatest value and your least value.
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