Contents

**Precision|Definition & Meaning**

**Definition**

**Precision** measures the **closeness** of a group of values (usually measured as part of an experiment) but ignores the truthfulness of the values in the process (called accuracy). Measuring precision helps us identify the consistency of an experimentâ€™s results. Alongside **accuracy**, the two quantify the** overall quality** of the experimentâ€™s results.

**Precision** measures the **percentage** of instances or **samples** that are rightly classified among those that are categorized as **positives**. The formula for **precision** is defined as **true** positives divided by **false** positives, or:

Precision =Â TP / (TP + FP)

**Difference Between Precision and Accuracy**

We frequently use phrases like **“****spot**** on”** and **bullseye**. These sentences typically appear when one deduces the correct answer to a query. How closely a **measurement** resembles the “**actual**” value is indicated by the data’s **accuracy**

For instance, the **time period** of a simple **pendulum** is 0.8 seconds. When student A calculates it using the **apparatus** in the laboratory, it comes out to be 0.74 seconds, while student B calculates it to be 0.78 seconds. We can say the latter has a more **accurate** reading.

Now, let us consider the **bullseye** as an illustration. The very center of the **target**, which is the “**actual**” value, must be struck in order for one to be judged to have thrown a dart with great **accuracy**.

However, if a shot repeatedly misses the **center** of the target, it would be seen as **inaccurate** because it is far from the “**actual**” value. Therefore, **accuracy** will **decrease** the further one goes from the center.

The hit is **far** from the **center** when the darts are thrown off. But one always strikes the same place. In this instance, the person was **precise** rather than **accurate**. The **agreement** of **multiple** testing is what is meant by **precision**.

If the darts neither hit the bullseye nor fall close to each other, then there is no **precision** as well as **accuracy**.

As a result, **precision** demonstrates how **frequently** the same **measurement** would be obtained under **identical** conditions, while **accuracy** indicates how **near** one was to the **actual** value. **Precision** is frequently referred to as **reproducibility** or **repeatability** by experts.

The more **accurate** you are, the **closer** you are to the **target** value. You must have well-defined goals or performance targets to establish **accuracy**.

To check for **precision**, provide a monitoring system that illustrates how numerous findings or **statistics** compare to one another over time.

In short, **precision** alludes to the **consistency** of the answer, whereas **accuracy** indicates the **correctness** of the solution.

**Importance of Precision in Measurement**

**Imprecise** measurements can **frequently** lead to **rework** or even more **drastic** measures, such as **restarting** a project entirely. As a result, **precise** measurement data is one of the main **information** sets that can help assure a **solid** project plan throughout the early stages of a **project**.

To obtain the most **consistent** results from a **scientific** investigation, it is critical to reduce **bias** and **errors** while also being **precise** and **accurate** in data gathering. **Precision** and **accuracy** are both concerned with how **near** a measurement is to its **real** or actual.

Modern **engineering** is heavily reliant on **precise**, convenient **measurements **in design, **building**, and **communication**, and modern **measurements** rely on **quantum** standards of frequency, wavelength, voltage, and other parameters.Â

The highly **precise** measurements made possible by these techniques have numerous applications, including the **study** of matter structure, geophysics, and astronomy.

**Precision-inscribed** components are required in numerous **industries** to guarantee that **electronics** and **engines** function smoothly, that **automobiles** and **aircraft** stay where they are supposed to be, that **technology** aids rather than hinders our lives, and much more.

**Measurements Should Be Both Precise and Accurate**

The implications of **precision** and **accuracy** go hand in hand. A **measurement** can be **precise** but **inaccurate,** and vice versa. We decide based on **precision** when observing **changes** in a process. When striving to reach a goal, **accuracy** is critical.

Suppose a group of students has developed a shared **database** in order to have **access** to reporting in a **centralized** manner and elevate the level of participation.

If they are extremely **accurate** but not quite as **precise**, they will create the database but may only notice an increase in **collaboration** between one or perhaps two projects.

If they are simply concerned with **precision**, they may add many **comparable** entries to the database. However, they may not be the ones on which your group needs to work.Â

If they were to create a database that is neither **precise** nor **accurate**, only one person would have access to it, which **discourages** collaboration.

It it is **precise** as well as **accurate**, then they have created a shared database with a slew of projects that are simple to work on as a group. Because the system is **reproducible**, they may continue to **cooperate** on many different projects as they arise.

**Examples of Precision in Sets of Measurements**

**Example 1**

Person A and person B are both assigned the task of measuring the length of a room five times. When person A measures it, the values are: 10.3 m, 10.4 m, 10.5 m, 10.6 m, and 10.7 m. When person B measures the length, the values are 10.0 m, 10.7 m, 10.9 m, 11,1 m, and 11.3 m.

Â Which person has the more measurements?

**Solution**

Let us calculate the average of lengths calculated by both persons.

Person A:

Average length = (10.3 + 10.4 + 10.5 + 10.6 + 10.7) / 5 = 10.5

Person B:

Average length = (10.0 m + 10.7 m + 10.9 m + 11.1 m + 11.3 m) / 5 = 10.8 m

As 10.5 m is closer to the measured values, person A has the more precise measurement values.

**Example 2**

Sonny and Ally performed an experiment to measure the density of copper (8.96g/mL). They come out with the following results:

Sonny: 8.52, 8.95, 8.68 and 8.21

Ally: 8.81, 8.84, 8.91, and 8.87Â Â

**Solution**

As we can observe from the values, when Ally performed the experiment, the values were close to each other. Hence, we can conclude Ally has measured the precise values.

**Example 3**

A binary model produces predictions and estimates 250 specimens from a segment, 170 of whom are correct, and 80 are erroneous. Determine the precision of this model.

**Solution**

Using the following formula, we can calculate the precision of the model:

TP/ (TP + FP)

TP (True Positive) = 170

FP (False Positive) = 80

Precision = 170/170 + 80 = 0.68 or 68%.

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