The relative percent change (the relative percent increase or decrease):
1. The absolute difference (the actual change). 2. The relative change. 3. The relative percent change. 4. Why do we use |v1| for the reference value instead of the value of v1? 5. Examples
1. The absolute difference (the actual change):
- The difference between two numerical values:
- v2 - v1
- ... is called the absolute difference, the actual change or the actual difference.
- When the value of v1 is the reference value (the starting value that the value of v2 is compared to) then the difference between v2 and v1 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 from the number 8 to the number 9 is of much more significance than the same difference of one unit between the much larger numbers of 9,999,998 and 9,999,999.
- In this case we need to take into account the "size" of the quantities involved.
- That's why we need a better indicator to compare two values, The Relative Change:
2. The relative change (from a number v1 to another number, v2):
- The relative change:
- the difference in an indicator 'v' over two periods in time, (v2 - v1), relative to the value of the indicator in the earlier period, v1:
- (The absolute change from v1 to v2) / |v1| =
- (v2 - v1) / |v1|
- ... where v1 is the reference value that v2 is being compared to,
- ... and |v1| is the positive value of v1; |2| = 2, |-2| = 2, |12| = 12, |-12| = 12.
- See below, at point 4, why do we use the value of |v1| instead of the value of v1.
- For values v2 larger than the reference value v1, the relative change is a positive number, and in this case we have a so called relative increase.
- For values v2 that are smaller than the reference v1 value, the relative change is negative and in this case we have what it's called a relative decrease.
- The relative change is not defined if the reference value is zero, v1 = 0.
3. The relative percent change
- The relative percent change is the Relative change calculated as a percentage;
- The relative percent change = The relative change × 100/100 = (The relative change × 100)%.
4. Why do we use |v1| for the reference value instead of the value of v1?
- The relative change: (v2 - v1) / |v1|
- Let's see what happens with the Relative Change indicator if we use v1 instead of |v1| in the formula above:
- Let's say that the initial value, the reference, is negative: v1 = - 2.
- Choose a random positive number for the end value, let's say v2 = 3.
- (v2 - v1) / v1 =
- (3 - (- 2)) / - 2 =
- (3 + 2) / - 2 =
- 5 / - 2 =
- - 2.5
- Although the absolute change is positive: 5, the relative change is negative: - 2.5!
- By using |v1| instead of v1, the error is corrected:
- (v2 - v1) / |v1| =
- (3 - (- 2)) / |- 2| =
- (3 + 2) / 2 =
- 5 / 2 =
- 2.5
5. Examples of calculating the relative percent change (increase or decrease)
- The relative change (from 2 to 3) = (3 - 2) / |2| = 1/2 = 0.5 = 50%
This change is a relative percent increase. - The relative change (from 9,999,999,998 to 9,999,999,999) = (9,999,999,999 - 9,999,999,998) / |9,999,999,998| = 1/9,999,999,998 ≈ 0 = 0%;
- The relative change (from 2 to -3) = (-3 - 2) / |2| = -5/2 = -2.5 = -250%
This change is a relative percent decrease. - The relative change (from 9,999,999,998 to -9,999,999,999) = (-9,999,999,999 - 9,999,999,998) / |9,999,999,998| = -19,999,999,997/9,999,999,998 ≈ -2 = -200%
This change is a relative percent decrease. - The relative change (from -2 to 3) = (3 - (-2)) / |-2| = (3 + 2) / 2 = 5/2 = 2.5 = 250%
This change is a relative percent increase. - The relative change (from -9,999,999,998 to 9,999,999,999) = (9,999,999,999 - (-9,999,999,998)) / |-9,999,999,998| = (9,999,999,999 + 9,999,999,998) / 9,999,999,998 = 19,999,999,997/9,999,999,998 ≈ 2 = 200%
This change is a relative percent increase.