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# Accuracy|Definition & Meaning

## Definition

**Accuracy** is a term used to define how **close** different **results **or **attempts** are as close to the **correct value**. Let us take an example of a reading of the** thickness of metal**. The correct value is close to 1mm. but the physical measurements read either 1.3 mm, 1.2 mm, or 0.8 mm. Hence, this concludes that the tool is **accurate** to about **0.3 mm** of the **true value**.

Furthermore, this means that if a **measuring device** gives a very different value from the actual value, it is **inaccurate** and **faulty** for usage. Furthermore, if a device gives measurement values closer to the actual value, it is considered to be **accurate**.

## Accuracy and Precision

Usually, **accuracy** and **precision** go hand in hand. Where accuracy is the closeness of a measured value to a true value, **precision** **means how** **close the measured values are to one another**, **irrespective of the actual value. **

There are certain cases where measured values are considered **inaccurate but are precise.** This means that the values are close to one another but are **far away** from the actual value. In another case, measured values are accurate but are not **precise.** This implies that the values are close to the actual value but are far away from each other.

## Errors

**Errors are the difference between a measured value from its true value.** A **high error** value means that the measuring device is **inaccurate** and vice versa is also true. Furthermore, there are** two types of errors** that can hinder the accuracy of data **calculated** or **measured.** These two errors are:

**Systematic Error****Random Error**

The **systematic error** implies that there is a systematic **defect** in the device that causes the results to be inaccurate but are all **precise.** This means that there is a “**bias**” caused by the measuring device.

Random Errors imply the **randomness** in errors caused by the **random effect** of **external natural factors,** such as air or the way the measurement is taken causing the error to be random. Hence these errors are **hard to remove** and give an accurate result. They are usually **not** precise.

## Significance of Accuracy

As stated above, accuracy is basically how close the value is to the correct value. Now, this accuracy can have multiple applications in innumerable fields of science and statistics.

Let us take an example of measuring a **length of a bar**. The correct length of a bar is stated to be **1.5 meters**. After using a measuring tape to measure the length about 3 times, we get the following results: **1.6 m, 1.55 m, and 1.45 m**. The values are fairly close to the actual value, hence they are considered somewhat **accurate.**

Furthermore, we can take multiple measurements to find an **average value** of these measurements, which will further give a more **accurate** result.

The range at which there is an error between the original and measured value is called the **“tolerance value.”** This is usually expressed as **“x value** $\pm$ **”tolerance value.”** They are commonly used in defining a standard for measuring instruments and devices and express how accurate they are in measuring **unknown** values.

### Accuracy in Other Applications

Moreover, accuracy also can be used in **statistics** and **numerical analysis** where **several sample data** are taken by different **calculation methods** and have a certain accuracy to their results. Errors in these calculations are usually caused by **approximations** taken in **calculations.**

When constructing a new measuring device or calculation method, we first take **multiple samples** of the **measured value** and then **calculate** its error and tolerance value from the actual **reference** value.

For example, let us say we are **constructing an ammeter** to measure current. From the multiple samples taken when measuring a value of **15 Amperes,** we find that the ammeter had a maximum error of **0.5 Amperes**. This means that the tolerance value of this **ammeter** is $\pm$**0.5** **amperes,** or we can say it is **accurate to 0.5 A.**

## Visual Representation Using a Dartboard

It is better understood when a visual aid is provided to explain **accuracy** and **precision.** The Figures below will give you a better insight into the **fundamental** meaning of the term accuracy and precision.

Here we consider a **target** with the center of the circles being the true value. **Figure 1** shows that the attempts on hitting the target were **far away** and **scattered** amongst themselves. Hence, they are having a **low accuracy** and as they are far from each other, they have **low precision. **

In our 2nd case, as shown in **Figure 2**, we can observe that the attempts are far away from the **intended target** (the center of the circle). Hence, the attempts are** low in accuracy**. However, these attempts are close to one another. Thus, we can conclude that the attempts are **high in precision**. This might imply that there is a **systematic error** or a **bias** in the attempts that can be **fixed by removing the source of bias. **

In our 3rd case, as per **Figure 3**, we can see that the attempts are **close** to the intended target and they are also close to each other. Hence, we can conclude that the attempts are **highly accurate and precise**.

## Finding the Accuracy of Given Data – An Example

Consider a set of values:** 12, 15, 13, 14, 13, 15. **The **reference value** that is true for this case is **13.5**. Conclude whether this set of values is **accurate or not.** If they are accurate, find their **tolerance value** as well. Are they **precise?**

### Solution

The set of values **12, 13, 14, 13, 15, and 15** are **close** to the true value of **13.5**. Hence, they are **accurate.**

Their **tolerance value** is found by calculating the **highest possible error.** In our case, the **farthest** value in the set from the true value is **12 and 15**. **Subtracting** them from the **original** value, we get 13.5 -12 = 1.5 or 15 – 13.5 = 1.5. Hence the resulting value can be written as **13.5** $\mathbf{\pm}$** 1.5**.

The values are fairly **close** **to** **each other**, so they can be considered **precise.**

*All mathematical drawings and images were created with GeoGebra.*