34 50 61 77 99 26 15 62 44 74 88
is 99 - 15 = 84
For example, consider the set of numbers we used above in the range example. First, arrange them in order:
15 26 34 44 50 61 62 74 77 88 99
Now, find the middle value. One simple way is just to start counting at both ends, crossing out a number at each end until you arrive at the middle value.
A formula way of arriving at the middle term is this:
middle term = (N + 1) / 2 , where N = the number
of values. In this example, N = 11, so
middle term = (11 + 1) / 2
which is 12 / 2, or 6. So the middle term
will be the 6th term, which correlates to the value 61.
Therefore, 61 is the median.
Now, suppose there is an even number of values. Consider the following set of numbers.
18 15 11 14 12 17 16 14 17 13
there are 10 values. Arranged in order, they look like this:
11 12 13 14 14 15 16 17 17 18
However, there is no exact middle term. It would fall between the second number 14 (the fifth term) and the number 15 (the sixth term). Therefore, the median would be the mean of the two terms, or 14.5.
Third Quartile: The third quartile of a set of numbers is the value in which 75% of the numbers are below it, 25% of the numbers are above it when the numbers are arranged in ascending (increasing) order.
Another way to think of the quartiles is this: The first quartile is the median of the numbers located below the median; the third quartile is the median of the numbers above the median. This may sound confusing, but it is easy to understand once a few examples are used:
For instance, look at the first set of numbers we used, arranged in ascending order. Remember 61 is the median. Note how the median (61) divides the numbers into two equal groups:
15 26 34 44 50 61 62 74 77 88 99
The numbers below the median are 15 26 34 44 50. The median (middle value) of those numbers is 34. So, 34 is the first quartile. Similarly, the numbers above the median are 62 74 77 88 99. The median (middle value) of those numbers is 77. So, 77 is the third quartile.
Highlighting each quartile and the median, you can see how they divide the numbers into four equal groups:
15 26 34 44 50 61 62 74 77 88 99
The second set of data we used, arranged in order, looked like this. Remember, the median of this set was not a number in the set; rather it was a number between two other numbers (14.5 = *).
11 12 13 14 14 * 15 16 17 17 18
So, the numbers below the median, 11 12 13 14 14, have a median of 13. So, the first quartile is 13. The numbers above the median, 15 16 17 17 18, have a median of 17 (the first one). So, the third quartile is 17.
Again, highlighting each quartile and the median, you can see how they divide the numbers into four equal groups:
11 12 13 14 14 * 15 16 17 17 18
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