Percentage Error

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The percentage error is the difference between the estimated and actual values compared to real values and is expressed as percentages. In other words, you take the difference between the real answer and the guessed answer, divide it by the real answer, and convert it into a percentage.

The percentage of errors indicates how significant our errors are when we measure something in the analysis process. A small percentage error means close to an acceptable or actual value. Measurement errors are often avoided for some reason, such as shaking hands, equipment may be accurate, or our tools may not have direct measurement capabilities.

The error can occur due to many different reasons, usually related to human error. Still, it can also be due to the limitations and limitations of the devices used. However, it is essential to calculate the percentage error in such cases.

Percentage Error

Percentage Error Formula

Percentage error is the difference between the estimated and exact values, divided by known value and multiplied by 100%. In most systems, the percentage error is expressed as a positive value. Generally, the total error is divided by the received value and is given as a percentage. This is how we come to the Percentage Error formula.

percent error formula

How is the percentage error calculated?

There are certain steps through which you can calculate the percentage error:-

  • Subtract one value from other values. Here the order does not matter. This number will be the error number.
  • Divide the error by the number of theories.
  • Convert the decimal number as a percentage by 100 times. It'll help to find out the percentage error rate.

What is a good percentage error?

The value of the test is your calculated value and the theoretical value of your known value. The percentage closest to zero means that you are very close to your target value, which is a good thing.

The percentage of errors tells you how big your mistakes are when you rate something on a test. Low values mean you are close to an acceptable or actual weight. For example, 1% error means you are more relative to the excellent value, and 37% points more immediate than the real value.

Benefits of finding percent errors

  • There are many benefits to finding percentage errors. A few advantages of finding percentage errors are given here:
  • Percentage error is essential for accuracy. Accuracy means the relative value of a relative value to its original value.
  • The error percentage is calculated by dividing the difference between the approximate and actual values by the real value and multiplying by 100.
  • The essential benefit of finding a percentage error is knowing how close you are to the actual value.
  • The error percentage may be as low as negligence or as high as your awareness. So, if the percentage error is too low you can ignore it, but if the percentage error is high, you have to calculate or quantify things to get the total value.

Solved Examples

Q1. Amit measured his height and found 6 feet. But later on, by careful observation, he has found his actual height to be 5.5 ft. Find the percentage error he made.

Ans. Before solving the problem, let us identify the information:- Actual value: 5.5 ft and Estimated value: 6 ft.

Now,

Step-1: Subtract one value from others to get the absolute value of error.

Error = ∣5.5 − 6∣ = 0.5

Step-2: Divide the error by actual value.

0.5∕5.5 = 0.0909 (up to 4 decimal places)

Step-3: Multiply that answer by 100 and attach the % symbol to express the answer as a percentage.

0.0909 × 100 = 9.09

Percentage error = 09.09%

Q2. Maria's English class had 25 students yesterday. She miscounted the class total and recorded it as 20 students. What is Maria's percent error?

Ans. The actual number of students: 25 and Recorded number of students: 20

Absolute Error = 25 - 20 = 5

Percent Error = 5/25 = 0.20

= 0.20 × 100 = 20%

Maria's percent error is 20%

Q3. John thought 50 people would turn up to the event organized. But on the day of the performance, only 60 people came. Find out John's percentage error?

Ans. The actual difference is= 50 – 60 = 10

Then apply the formula,

Percentage Error = 10∕60×100

= 16.66 %

John was having errors of 16.66%.

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