The percentage error formula calculates the difference between the estimated number and the actual number compared to the actual number. It is expressed as a percentage. In other words, it is simply the difference between the real and assumed numbers in a percentage format.
In Science-related matters, the percentage error formula is often used wherein determines the variance between the experimental value and the exact value. This calculation will help us compare a value derived from the experiment with an exact or true value. The percentage error also provides information on how close one is in their measurement or their estimation of the true or the real value.
The percent error formula calculates the difference between an estimated number and the actual number relative to the actual number itself.
The result is expressed as a percentage, providing a measure of the magnitude of the error.
The percent error calculation is a straightforward yet valuable tool, as it provides a quantifiable representation of the mistake made.
It can be employed whenever it is essential to assess the level of error in data, allowing for the identification of equipment malfunction, personal errors, or inaccuracies in assumptions or estimations.
Percent Error Formula Explained
The percentage error formula is used to find the difference in the measured or estimated value and the true value. It is expressed as a percentage of true value. It is extensively used in any kind of scientific experimentation or in any other fields where some measurement of forecasting is done to assess the level of accuracy.
This tool is very useful for identifying any kind of deviation between the actual value and the estimated value. Thus, it also helps in determining or identifying the degree or extent of error.
Here it is to be noted that the if the outcome is zero, then it show a perfect level of accuracy. If the percentage is more than zero, it indicates that the estimated value is more or less than the actual value. If the actual value is more than the estimate, then the percentage error will be negative.
It is useful but it also has its own limitations. Therefore, it should be used along with other relevant prevalent methods for assessing the accuracy level of predictions or measurements.
The formula for the calculation is given below.
PE = |Experimental Value - Exact Value| / |Exact Value| * 100
How To Calculate?
To calculate the percent error, one can follow the below steps:
The first must obtain the experiment (assumed) and exact values.
Find the variance between them and then take the absolute value; one needs to ignore any negative sign. It is known as the error.
Next, find out the absolute value of the exact or true value.
Divide the absolute error (non-negative), determined in Step 2, by the absolute true value or the exact value.
Finally, multiply the result obtained in step 4 by 100 so that the result converts into a percent value, and then add a “%” symbol to the result.
Examples
Let us look at some examples to understand the concept in detail.
Example #1
A new tourist place, the Statue of Unity, was recently established in Gujarat, India. They estimated that around 3,00,000 people would turn around on its inauguration day. But the number of people that came for its inauguration was around 2,88,000. So, you are required to calculate the percentage error. Below is given data for the calculation of the percent error.
Therefore, the calculation of the percent error will be as follows:
=(300000-288000)/288000*100
Percent Error will be –
Percentage Error= 4.17%
Example #2
Avenue Supermarket, a retail company operating under the name “Dmart,” is in an expansion phase, and the company plans to open new branches in new cities. The company planned and estimated to open 24 branches at the start of the financial year. However, by the end of the year, the company opened only 21 stores. As a result, the company has approached you to calculate the percentage error they made during initial planning.
Below is given data for calculation of Percent Error
Therefore, calculation of the Percent Error will be as follows,
=(24-21)/21*100
Percent Error will be –
Percentage Error= 14.29%
Example #3
As per a poll by a news channel during an election campaign, they estimated that XYZ party would win 278 seats out of 350 seats. After the results came out, it turned out that the XYZ party managed to win 299 seats out of 350 seats. The news channel is perplexed by the actual outcome and wants to know what margin error they made and how much they lagged. Calculate the percentage error.
Below is given data for the calculation of Percent Error.
Therefore, the calculation of the percent error will be as follows:
Percent Error will be –
Percentage Error=-7.02%
Uses
The percent error appears to be a simple calculation, but it is very useful as it provides us with a number that will depict our error. Further, it is used whenever it is crucial to know the amount of error which is present in the data, and it is necessary to know the reason for the error, whether the reason is due to by equipment impairment or by one’s own error or mistake in the assumptions or estimations.
The formula can be used in various fields. Here are some uses of the formula.
Experiments – It is used in various experiments to understand the accuracy level of the results. When the estimated values are compared with the actual values, the degree of error is identified and it is possible to make necessary adjustments to improve the accuracy level.
Quality Control – During the production process of goods, this formula is used to identify inconsistencies or defects in the product and help in maintaining quality standards.
Financial predictions- Financial analysts use this method for assessing the financial condition or performance. The formula helps in finding the deviations or errors in the model so as to get forecasts accurately.
Climate modelling – The models used to forecast climates also use this method to identify errors. This helps in improving the analysis and making predictions that the best in quality.
Use in sports – It is also used in statistics related to sports to compare the performance of various athletes.
Thus the above points describe in detail the main uses of the formula.
Frequently Asked Questions (FAQs)
1. What are the applications of the percent error formula?
The percent error formula finds application in various fields, including scientific experiments, data analysis, quality control, and financial forecasting. It allows for the comparison of estimated or measured values to a known or expected value, helping to assess the accuracy or precision of measurements, forecast accuracy, and the quality of experimental or analytical results.
2. What are the limitations of the percent error formula?
The percent error formula has a few limitations. It assumes that the known or expected value is accurate, which may not always be the case. It does not account for systematic errors or uncertainties in measurements. Additionally, the percent error calculation is sensitive to small changes in values, which can lead to larger percentage errors.
3. Why do we calculate percent error?
We calculate percent error to quantify and express the difference or discrepancy between an estimated or measured value and a known or expected value. It allows us to assess the level of accuracy or precision in measurements, experiments, predictions, or estimations. By calculating the percent error, we can identify the magnitude and direction of the error, helping us understand the reliability and quality of data or results.
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