How to calculate Percent Error? Percentage error is an estimation of the inconsistency between a noticed and a valid or acknowledged esteem. While estimating information, the outcome regularly shifts from genuine worth. The error can emerge because of a wide range of reasons that are regularly connected with human error yet can likewise be because of assessments and limits of gadgets utilized in the estimation.
Percent error is the difference between the estimated value and the actual value in comparison to the actual value and is expressed as a percentage.
This article will guide you through the process of how to calculate percent error in various contexts.
What Is Percent Error?
Percent/Percentage error is the distinction between the actual value and the estimated value contrasted with the actual value and is communicated in a percentage design. All in all, you track down the distinction between the actual response and the speculated reply, partition it by the actual response, and express it as a percentage. Percent errors demonstrate how gigantic our errors are at the point at which we measure something. For example, a 3% error demonstrates that we got extremely near the acknowledged value, while 80% implies that we were very a long way from the actual value
In simple words, Percentage error is the contrast between a deliberate and exact value, isolated by the known value, and subsequently increased by 100 percent. For some applications, percentage error is communicated as a positive value. Regularly, the absolute value of the error is partitioned by an accepted value and given as a percent.
The formula for finding percent error,
Percent Error = (Actual Value – Estimated Value)/(Exact value) × 100
Most of the time, the percentage error is expressed as a positive value.
Actual value can be a few times named as true value or exact value.
How to Calculate Percent Error?
Percentage error can be determined utilizing three straightforward advances,
- Work out the error (Deduct assessed esteem from the real worth) and disregard any negative (-) sign. i.e., take the absolute worth of error.
Absolute Error = Approximate Value – Exact Value
- Partition the error by the real worth (in some cases, we might get a decimal number).
Relative Error = (Approximate Value – Exact Value )/( Exact Value)
- Convert that to a percentage (by increasing by 100 connect “%” sign)
Percent Error = {(Approximate Value – Exact Value )/( Exact Value)} × 100 percent.
The absolute worth of the error is separated by a genuine worth and displayed as a percent.
Steps to Calculate Percent Error
Identify the Measured and True Values: The first step in calculating percent error is to identify the measured (or experimental) value and the true (or accepted) value.
Subtract the True Value from the Measured Value: Subtract the true value from the measured value. The order of subtraction doesn’t matter because we will be taking the absolute value of the result.
Divide by the True Value: Divide the result from step 2 by the true value.
Multiply by 100%: Multiply the result from step 3 by 100% to convert the decimal to a percentage.
How to Calculate Percent Error – Solved Examples
Question 1: Mr. Raju 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 percent error Raju made in measuring his height.
Solution:
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]e of error.
Error = 6 – 5.5
= 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%
Therefore Percentage error measured is 9.09%
Question 2: Lakshmi’s mathematical class had 34 children yesterday. She miscounted the class total and recorded it as 28 children. What is Lakshmi’s percent error?
Solution:
The actual number of students = 34
Recorded number of students = 28
Absolute Error = 34 – 28 = 6
Percent Error = 6/28 = 0.21
= 0.21 × 100 = 21%
Lakshmi’s percent error is 21%
Question 3: A boy measured the area of a rectangle plot to be 450 cm². But the actual area of the plot has been recorded as 455 cm². Calculate the percent error of his measurement.
Solution:
Given,
Measured area value = 450 cm²
Actual area value = 455 cm²
Steps of calculation,
Step 1: Subtract one value from another; 455 – 450 = 5
the difference is 5, which is the error.
Step 2: Divide the error by actual value; 5/455 = 0.0109
Step 3: Multiply this value by 100
0.0109 × 100 = 0.109% (expressing it in two decimal points)
Hence, 0.10% is the percent error.
Question 4: A scale measures wrongly a value as 21 cm due to some marginal errors. Calculate the percentage error if the actual measurement of the value is 17 cm.
Solution:
Given in the problem,
Recorded measurement = 21 cm
Actual measurement = 17 cm
Error = Recorded measurement – Actual measurement
= 21 – 17 = 4
Applying the formula for the computation,
Percentage Error = (Error) / (Actual measurement) × 100
= (4/17) × 100 = 0.235 × 100 = 23.5
Percentage Error calculated as 23.5%
Question 5: John expected 30 people to turn up for a job interview, but only 24 did. What was the percentage error?
Solution:
The actual number of people attended = 24
Number of people expected = 30
Absolute Error = 30 – 24 = 6
Percent Error = 6/30 = 0.20
= 0.20 × 100 = 20%
John’s percent error is 20%
Question 6: Sam thought 90 people would turn up to the concert, but in fact, 100 did. What would be Sam’s percent error?
Solution:
The actual number of people came to concert = 100
Number of people Sam expected = 90
Error = Expected number of people attended – Actual number of people
= 100 – 90 = 10
Applying the formula for the computation,
Percentage Error = (Error) / (Actual measurement) × 100
= (10/90) × 100 = 0.235 × 100 = 23.5
Percentage Error calculated as 23.5%
Question 7: Shreya is attempting the precision of a scale in her science lab. She took a weight that she knew had a mass of 30 kg and weighed it. The scale read that the weight weighed 30.4 kg. What is the absolute error of the mass of the weight that Shreya recorded? And also find percent error?
Solution:
Use the absolute error formula to determine this,
Absolute Error = |Actual Value – Measured Value|
Absolute Error = x
Actual Value = 30
Measured Value = 30.4
= |30 – 30.4| = |−0.4| = 0.4
The absolute error was 0.4 kg.
Percentage Error = (Error) / (Actual value) × 100
= (0.4/30) × 100
=1.3333% (Considering upto 2 decimal points)
Therefore Shreya’s percent error is 1.33%
Practice Problems on How to calculate Percent Error
Conclusion – How to Calculate Percent Error
Percent error is a useful tool in science and engineering to quantify the accuracy and precision of measurements. By understanding how to calculate percent error, we can better interpret the results of experiments and measurements.
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FAQs on How to Calculate Percent Error?
What does a high percent error indicate?
A high percent error indicates a large discrepancy between the measured and true values, suggesting a less accurate measurement.
Is a lower percent error always better?
Generally, a lower percent error indicates a more accurate measurement. However, it’s important to consider the context and the acceptable margin of error for the specific situation.
Can percent error be negative?
No, percent error is always expressed as a positive value. This is because we take the absolute value in the formula, which removes any negative sign.
What factors can contribute to percent error?
Factors that can contribute to percent error include human error, instrument precision and calibration, and the inherent variability in the system being measured.
How can we reduce percent error?
Percent error can be reduced by improving measurement techniques, using more precise instruments, and repeating measurements to average out random errors.
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