Can median only be determined in a set of numbers ordered from least to greatest?

Question

Is it only possible for a median of a set of numbers to be detemined if the set of numbers is arranged from least to greatest?

Answer 1

It's EASIEST to do it that way, but it is not required.

You could write a computer program that found the median from an unsorted list by trial-and-error (guess the first entry in the list, then go through the entire list and count how many entries were larger and how many were smaller; if the first entry wasn't the median, guess the second entry in the list, and so on...).

But that is inefficient for large lists.

As a counter-example of a different type, I can tell you the median from this list:

(100, -100, 50, -50, 0)

... without having to sort it. I bet you can tell what it is, too.

Answer 2

By definition, the median is the middle number in an ordered set (or the average of the two middle values if the list has an even number of items). You could order them from greatest to least and get the same result.

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You can be crafty and use an order that is different from the classical order. However, your choice of "median" would be useless unless you also defined the order every time.

A= {8, 5, 4, 1, 7, 6, 3, 2, 0} is an ordered set, in the proper order.

The median of this ordered set is 7.
The order of A represents the order in which the names of the numbers 0 to 8 are found in an English language dictionary.
Not very useful in maths (however, someone could contrive some usefulness in a sorting program).

Answer 3

All you have to do is arrange the numbers in order from least to greatest OR greatest to least. Either way you get the same answer. For Example:
If your numbers are - 17, 3, 89, 54, 76 you would arrange them like this - 3, 17, 54, 76, 89 and the median would be 54 because it's in the middle.
You could also arrange them like this: 89, 76, 54, 17, 3 but either way the answer is still 54.

If you have a set of numbers where there are two numbers in the middle, you add them, then divide by two. For Example:
If your numbers are: 17, 3, 89, 48, 54, 76 you would arrange them in either greatest to least OR least to greatest (I like least to greatest): 3, 17, 48, 54, 76, 89 but 48 and 54 are in the middle! So you add them: 48 + 54 = 102
Then you divide 102 by 2: 102 divided by 2 = 51
So 51 would be your median. That is how I learned to do it, and it's really simple and easy to remember.

I hope I could help!

Answer 4

It doesn't matter whether it's least-to-greatest or greatest-to-least, the middle is STILL in the same spot.

1 2 (3) 4 5 - 3 is the median
5 4 (3) 2 1 -Look, 3 is sitll the median!

Answer 5

no duh! the median is found by arranging the numbers from least to greatest then taking the one in the middle for example if u have a set of four numbers 1,2,3,4 the median would be 2 and 3 so u would add them and then divide them by 2 and u'll the get the median

Answer 6

Just add them ALL up and divide by the number of numbers you have...for example

1
2
3
4
5
and the median is.....1+2+3+4+5 / 5

if it were
1 3 4 2 5, you would still be using the same numbers and the same amount of numbers, so the formula remains, add up all the numbers and divide by how many there are.

Answer 7

Solve 6(x + 1) - 4 = 3x + 2. 6x + 6 - 4 = 3x + 2 6x - 3x = 2 + 4 - 6 3x = 0 x = 0 answer Write the standard form of the equation of the line that is perpendicular to 3x - 2y = 5 and passes through (2,4). The given line : 3x -2y = 5 ..................... [1] -2y = -3x + 5 y = (3/2)x - 2,5 Slope = 3/2 So slope of the line perpendicular to [1] = -2/3 So let the required line is : y = (-2/3)x + c ................... [2] To find c the line passes through point (2, 4) 4 = -4/3 + c c = 4 + 4/3 = 16/3 Hence the required line is : y = (-2/3)x + 16/3 OR 3y = 16 -2x a n s w e r

Answer 8

No, you can order them from greatest to least as well.

And if you have a computer, you don't have to order them at all. A lot of computer software will order them automatically (without printing the results) before finding the median.

Answer 9

Yes, simply based on how you find a median. You don't necessarily have to write them down that way, you can just find the top number, cross it out, then the lowest number, cross it out, and so on.

Answer 10

yes