什么是百分比差异公式？
百分比差异公式以百分比形式查找任何数量的变化。它是初始值和最终值的绝对差除以它们的平均值并乘以 100 的比率。
特性：
- 它以 100 为单位计算值的变化。
- 它测量两个量之间差异的绝对值
- 它始终是一个正数。
- 它是一个无量纲的量。
公式
Percentage difference = Absolute difference/Average × 100
推导：
Lets, initial value be a and the final value is b.
Then average value is (a + b) / 2
The difference stands as (b – a).
The absolute value of this difference = |b – a|
So, the ratio of the above two is |b – a| / ((a + b) / 2) = 2|b – a| / (b + a)
So, the percentage difference stands as 2|b – a| / (b + a) × 100
因此，公式为：
Percentage difference = 2|b – a| / (b + a) × 100
示例问题
问题 1. 求 20 和 40 的百分比差异。
解决方案：
The average value is equal to (20 + 40) / 2 = 60/2 = 30
The absolute value of difference = |40 – 20| = 20
Thus, percentage difference = 20 / 30 × 100 = 66.67 %
问题 2. 如果汽车速度的初始值为 30 公里/小时，最终值为 60 公里/小时，求汽车速度的百分比差异值。
解决方案：
The average value of the speed = (30 + 60)/2 = 45 km/hr
The absolute value of the difference of the speeds = |60 – 30| = 30 km/hr
Thus, the value of the percentage difference = 30 / 45 × 100 = 66.67%
问题 3. 如果一个值为 70，并且百分比差异为 50%，则找到另一个值。
解决方案：
Let’s another value be ‘a’.
Given the other value is 70 and the percentage difference is 50%.
The average value stands as (a + 70) / 2.
The absolute value of the difference = |70 – a|
The percentage difference is |70 – a| / (a + 70)/2 = 2|70 – a| / (a + 70) × 100
Thus, we can write,
2|70 – a| / (a + 70) × 100 = 50
|70 – a| / (a + 70) = 0.25
There are two cases possible:
Case 1: If a > 70,
Then, |70 – a| = a – 70
So, we can write:,
(a – 70) / (a + 70) = 0.25
a – 70 = 0.25a + 70 × 0.25 = 0.25a + 17.5
a – 0.25a = 70 + 17.5
0.75a = 87.5
a = 116.67
Case 2: If a < 70,
Then, |70 – a| = 70 – a
(70 – a) / (a + 70) = 0.25
70 – a = 0.25a + 70 × 0.25 = 0.25a + 17.5
a + 0.25a = 70 – 17.5
1.25a = 52.5
a = 42
问题 4. 如果一个人把 45 写错了 54，求百分比差异的值。
解决方案：
The average value of the two numbers = (45 + 54)/2 = 99/2 = 49.5
The absolute value of the difference of the numbers = |45 – 54| = 9
Thus, the value of the percentage difference = 9/49.5 × 100 = 18.18 %