In quantitative analysis, percent deviation is a crucial concept to understand. It indicates the difference between an observed value and the true or expected value, showing how far that observation lies from the accurate value. This article will walk you through the process of calculating percent deviation step-by-step.

Step 1: Understand the Concept

Percent deviation helps you evaluate the accuracy of measurements or experimental data. It provides a measure of how far an observed result deviates from its expected outcome. The smaller the percent deviation, the closer your data is to the expected or true value, implying a more accurate measurement or result.

Step 2: Identify Observed and True Values

To calculate percent deviation, you need to know two values – observed value and true value. Observed value is the actual measurement or result you collected, while true value refers to what you expect based on a theoretical calculation or accepted benchmark.

Step 3: Calculate Absolute Deviation

Subtract the true value from the observed value to determine the difference between both values. The result may be positive or negative- however, it is important to use absolute values so that deviations do not cancel each other out in further calculations. Therefore, if negative, change it to a positive number.

Absolute Deviation = |Observed Value – True Value|

Step 4: Calculate Relative Deviation

Next, calculate relative deviation by dividing absolute deviation by true value. This method allows you to compare deviations of different measurements on a unified scale.

Relative Deviation = Absolute Deviation / True Value

Step 5: Convert Relative Deviation to Percent Deviation

Lastly, multiply relative deviation by 100% so that your result is expressed in percentage form.

Percent Deviation = (Relative Deviation * 100)%

Now you have successfully calculated percent deviation for your data!

Example Calculation:

Imagine you measure an object’s length and obtain 105 cm as the observed value. Based on a reference book, the length should be 100 cm (true value).

1. Calculate Absolute Deviation: |105-100| = 5 cm

2. Calculate Relative Deviation: 5 cm / 100 cm = 0.05

3. Convert to Percent Deviation: 0.05 * 100% = 5%

In this example, your measurement has a percent deviation of 5% from the true value.

Understanding and calculating percent deviation is essential for evaluating the accuracy of experimental data or measurements. With this guide as your reference, you can now confidently perform these calculations with ease.