Question

30,45,x,100; The median is 51

Answer 1

To solve for x, you must first understand how the median was calculated out of the given set of numbers. Without looking at the given median value, we can see that we cannot get the median by process of elimination since there are an even amount of numbers in this particular set. Therefore, we must average the two closest values to what should be the median.

In this case, the values are "45" and "x". If we pretend that we know the value of the variable "x" (for example we will pretend that x is 55), then we should have an equation that looks like this: (45+55) ÷ 2 = [median]. What this equation is doing is adding the two closest values to the median (45 and 55) and dividing it by 2, the number of values we are averaging. Now we can solve this equation and simplify it to 100 ÷ 2 which is 50, our median.

So if they give us the median instead of the x value, then we can rewrite the equation to fit your request: (45+x) ÷ 2 = 51. Now we can solve for x:

1. Multiply by 2
(45+x) = 102

2. Subtract 45
x = 57

The x value for your question is 57.

Answer 2

x = 57

Explanation:

Median is the number that is halfway mark. If we are given a data, first we need to arrange them in ascending order and take the middle value. That is called median.

If we have odd number of data, we can easily find the middle value.

For instance, 1, 2, 3, 4, 5 here the number of data = 5 which is odd number.

The middle number is 3.

Therefore, median is 3.

If we have even number of data, we have to take middle two values, add them then divide by 2.

In this case, we are given even number of data

30, 45, x, 100

4 data which is even number of data.

Median is given as 51, we need to find the value of x.

The middle two numbers are 45 and x, we have to add them and divide by 2

Median =
`(45 + x)/(2)` [Given: median = 51]

51 =
`(45 + x)/(2)`

Multiplying both sides by 2, we get

51*2 = 45 + x

102 = 45 + x

Subtract 45 in both sides, we get

102 - 45 = 45 -45 + x

x = 102 -45

x = 57