The relative percent decrease change. The absolute difference (the actual variation). Examples
The absolute difference (the actual variation):
- The difference between two numerical quantities, y - x, is called the absolute difference, the actual change or the actual difference.
- When y value is the reference value (the starting value that the value of x is compared to) then the difference between y and x is called the absolute change.
- The actual difference (the actual change) between two values is not always a good way to compare two numbers.
- The actual change of one unit between the numbers 3 and 2 is of much more significance than the same difference of one unit between the much larger numbers of 9,999,999,999 and 9,999,999,998.
- In this case we need to take into account the "size" of the quantities involved.
The relative decrease change from a number x to another number y
- The relative decrease (from x to y) = (The absolute variation from x to y) / |x| = (x - y) / |x|, where x is the reference value that y is being compared to and |x| is the positive value of x.
- For values y larger than the reference value x, the relative decrease is a negative number, and in this case we have a relative increase instead.
- For values y that are smaller than the reference x value, the relative decrease is positive, and in this case we really have a relative decrease.
- The relative decrease (change) is not defined if the reference value is zero, y = 0.
The relative percent decrease
- The relative percent decrease is the relative difference calculated as a percentage;
- Relative percent decrease = Relative decrease × 100/100 = (Relative decrease × 100)%.
Examples of calculating the relative percent decrease change
- Relative change (from 3 to 2) = (3 - 2) / |3| = 1/3 = 0.33 = 33%
This change is a relative percentage decrease; - Relative decrease (from 9,999,999,999 to 9,999,999,998) = (9,999,999,999 - 9,999,999,998) / |9,999,999,999| = 1/9,999,999,999 ≈ 0 = 0%;
- Relative decrease (from -3 to 2) = (- 3 - 2) / |-3| = - 5/3 = -1.67 = -167%.
The relative percent decrease is negative so we have in fact a relative percent increase; - The relative percent decrease (from -9,999,999,999 to 9,999,999,998) = (-9,999,999,998 - 9,999,999,999) / |-9,999,999,999| = -19,999,999,997/9,999,999,999 ≈ -2 = -200%
This change is a relative percent increase; - Relative percent decrease (from 3 to -2) = (3 - (-2)) / |3| = (3 + 2) / |3| = 5/3 = 1.67 = 167%
This change is a relative percentage decrease; - Relative decrease (from 9,999,999,999 to - 9,999,999,998) = (9,999,999,998 - (-9,999,999,999)) / |9,999,999,999| = (9,999,999,998 + 9,999,999,999) / |9,999,999,999| = 19,999,999,997/9,999,999,999 ≈ 2 = 200%
This change is a relative percentage decrease.