This is an easy question “What is the mean age of 11-15?” really but it’s worth for people to understand the different concepts and differences between “mean“, “arithmetic mean“, “statistical mean“, “average“, “midrange“, “median“, and “mode“.
The arithmetic mean and average are the same thing. So, if you find the average of the numbers 11 to 15 (inclusive), it is of course 65/5=13. That’s also the default “mean” when “arithmetic” or “statistical” prefix is not specified .
In statistics, its mean is calculated by adding the smallest and largest numbers and dividing the sum by 2. That’s technically called the midrange. In this case, (11+15)/2=13. They turned out to be same in this case, so the answer is 13. However, there are cases where statistical mean and arithmetic mean may not be the same!
Don’t confuse the median with mean or average though! The median is the number that appears smack in the middle of the data series when sorted! So, in this case, 11, 12, 13, 14, 15. Well, it’s easy and sorted in ascending order and we have 13 at the middle position…so, the median is 13. Nice! Everything is pointing to 13. Don’t fool yourself! It just happens that the person who posed this question picked this series where all of these have the same answer. If you memorize the number, you’ll be wrong in all other instances, so regardless of the result, remember the methods. What if the data series was: 11, 12, 13, 14, 14, 15, 15? What’s the median? Now you can easily know the answer as explained above.
Remember, you can ONLY find the perfect middle of a sorted series when the total number of data points is an ODD number. So what if the data points are EVEN numbers? Of course, in real-life we have to deal with both. So, what if the series was: 11, 12, 13, 14? There’s NO perfect middle position. In fact the only middle is shared by 12 and 13. In that case, the median would be the arithmetic mean of them!
Now, if you’re going to be mean about it, that’s a whole different matter as I’ve seen plenty of mean of people in the range of 11–15 years of age…Especially, in my post midlife, I’m not trying to be one, as I like to carry myself as just another average guy. (pun intended)
Exercise: Mode is a different thing altogether. It’s a number that occurs most frequently in a series. E.g. In a series 1,2,3,2,4,5 the mode is 2. So, what’s the mode of 11-15 (inclusive)?