The median of the following set of numbers is 31. find the value of x which occupies the 3rd position when the numbers are arrganged in ascwnding order. 34,43,35,17,23,x

Feel free to skip parts you already know.

FIND THE MEDIAN: I'll use a different set of numbers as examples.

5, 3, 8, 9, 2

Order your numbers*
2, 3, 5, 8, 9

Median = middle
Find the middle number of the set. For here, you delete a number from the outsides of your set until you have 1 or 2 numbers. Like so;
2, 3, 5, 8, 9
3, 5, 8
5

5 is the middle number, therefore, it is the median.

· · ·

An even set of numbers is more difficult since you will be left with two numbers.

8, 3, 5, 9, 2, 7

Order your numbers*
2, 3, 5, 7, 8, 9

Median = middle
Find the middle number of the set. For here, you delete a number from the outsides of your set until you have 1 or 2 numbers. Like so;
2, 3, 5, 7, 8, 9
3, 5, 7, 8
5, 7

After you are left with 2 numbers, add them together and divide by 2.

5 + 7 = 12
12 ÷ 2 = 6

6 is the median of this set.

If the two numbers are equal to an odd number, it will have a decimal.

*Ascending order is usually implied for solving median.

EQUATION:

34, 43, 35, 17, 23, x

Order your numbers:
17, 23, x, 34, 35, 43

We now know x is a number between 23 & 34.

To solve for x, understand the problem.
You need to have the median be equal to 31, and since this is an even numbered set, you need to add the two in the middle and divide by 2.

17, 23, x, 34, 35, 43
23, x, 34, 35,
x, 34

Now we know x is part of the problem. So, let's make an equation.

(x + 34) ÷ 2 = 31

SOLUTION:

x + 34 should be equal to 31 · 2 (since the average is 31) which is 62.
Subtract already known number.
62 - 34 = 28

28 is the answer. Just in case there was a mixup, let's check our work with that equation.

(28 + 34) ÷ 2 = 31
62 ÷ 2 = 31
31 = 31 ✔

x = 28