# What are Accuracy and Precision? – Examples, Difference, Measurement

## Introduction to Accuracy and Precision

Have you ever wondered how scientists, engineers, and even your favorite chefs make sure they get things just right? Whether it’s measuring ingredients for a perfect cake or ensuring a spacecraft lands exactly where it should, accuracy and precision play a vital role. In this article, we’ll explore what accuracy and precision are, how to measure them, and their key differences, all in a way that’s easy to understand. So, let’s dive into the world of accuracy and precision!

## What is Accuracy?

Accuracy is all about how close a measured value is to the true or accepted value. It tells us how well a measurement reflects reality. If you shoot a basketball into a hoop and it goes through the net, you’re accurate. If you miss the hoop entirely, you’re not very accurate.

### How to Measure Accuracy?

To measure accuracy, you need to compare your measurement to a known or true value. Let’s say you have a scale at home, and it claims to weigh things accurately. You can test this by placing a known weight, like a 500-gram weight, on the scale. If it shows 500 grams, the scale is accurate.

Ex. Let’s say you’re measuring the length of an object with a ruler. You measure it to be 10.2 cm, but the actual length is 10.0 cm. In this case, the Accuracy of your measurement is 10.0/10.2, or approximately 98%.

Procedure to Measure Accuracy:

• Find a known or true value.
• Compare your measurement to the known value.
• Calculate the difference between your measurement and the known value.

### Accuracy Formula

The accuracy formula is quite simple. You calculate it by finding the absolute error and dividing it by the true value.

Formula of Accuracy

Accuracy = (|Measured Value – True Value| / True Value) x 100%

Now, let’s take a closer look at how this formula works.

Derivation:

• Find the absolute error: |Measured Value – True Value|
• Divide the absolute error by the true value.
• Multiply the result by 100% to express accuracy as a percentage.

## What is Precision?

Precision, on the other hand, focuses on the consistency and reliability of your measurements. It tells you how close your measurements are to each other. Imagine you’re throwing darts at a dartboard. If all your darts land close to each other, you’re precise. If they’re scattered all over the place, you lack precision.

### Procedure to Measure Precision

To measure precision, you need to repeat a measurement multiple times and see how close the results are to each other.

Procedure to Measure Precision:

• Take multiple measurements of the same quantity.
• Calculate the average of these measurements.
• Find the difference between each individual measurement and the average.
• Calculate the average of these differences.

This average of differences is called the “standard deviation,” which is a common way to measure precision.

### Precision Formula

The formula for precision involves calculating the standard deviation. It may look a bit complex, but it’s a way to quantify how spread out your measurements are.

Formula of Precision:

Precision = Standard Deviation

## Examples of Accuracy and Precision

Now, let’s see accuracy and precision in action with a few examples.

Example 1: Archery

Imagine you’re an archer aiming at a target. If all your arrows land very close to the bullseye, you’re both accurate and precise. But if your arrows land far from the bullseye and are also scattered around, you’re neither accurate nor precise.

Example 2: Baking

In baking, accuracy and precision matter a lot. If a recipe calls for 200 grams of flour and you measure 180 grams, you’re not very accurate. If you repeat this measurement several times and consistently get results like 180 grams, you lack precision as well.

Example 3: Astronomy

Astronomers use telescopes to study distant celestial objects. They need both accuracy and precision in their measurements. Accuracy ensures that they’re observing the right star or galaxy, and precision allows them to detect subtle changes in these objects over time.

## Difference Between Accuracy and Precision

Let’s summarize the key differences between accuracy and precision in a simple table:

 Aspect Accuracy Precision Focus How close to the true or accepted value a measurement is. How close repeated measurements are to each other. Goal Achieving the correct result. Reducing variation between measurements. Evaluation Determined by comparing a measurement to a known value. Determined by analyzing the spread of measurements. Example Hitting the bullseye with every arrow. All arrows landing in a tight cluster, even if it’s away from the bullseye. Formula Accuracy = (|Measured Value – True Value| / True Value) x 100% Precision = Standard Deviation

## Final Notes

Accuracy and precision are crucial in various fields, from everyday activities like cooking to scientific research and engineering. Understanding the difference between them and how to measure them can help you make better decisions, improve your skills, and achieve more reliable results in your endeavors. So, whether you’re a budding scientist, a future chef, or just someone who wants to be better at what they do, remember the importance of accuracy and precision in your measurements.

In summary, accuracy and precision are fundamental concepts that affect the quality of measurements in various fields. Whether you’re aiming for a bullseye, cooking a perfect meal, or conducting scientific experiments, understanding and achieving the right balance between accuracy and precision is essential for success.

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## FAQs

Define Precision

Precision is a measure of how close repeated measurements are to each other. It quantifies the consistency and reliability of measurements.

Accuracy Definition

Accuracy refers to how close a measured value is to the true or accepted value. It tells us how well a measurement reflects reality.

What is Accuracy Formula?

The accuracy formula is calculated by finding the absolute error (the difference between the measured value and the true value) and dividing it by the true value. It is expressed as a percentage.

Accuracy Formula:

Accuracy = (|Measured Value – True Value| / True Value) x 100%

What is Precision Formula?

The precision formula involves calculating the standard deviation of a set of measurements. The standard deviation quantifies how spread out the measurements are and, in turn, measures precision.

Precision Formula:

Precision = Standard Deviation