Contents

- Definition
- Degree Of AccuracyÂ
- Importance of Measuring Accuracy
- Measurement of Accuracy and Precision
- Collection of Data
- Average Value
- Percentage Error
- Absolute Deviations
- Average Deviations
- Use of Approximations in Real Life
- Degree of Approximations in the Construction Industry
- Examples of Measuring the Degree of Accuracy

# Degree (Accuracy)|Definition & Meaning

**Definition**

The degree of accuracy is a measurement of how close a given measurement is to the true value. It helps us identify the quality of measurements by checking that they are accurate.

**Scientists** and other **professionals** who analyze data to draw conclusions or assess hypotheses rely on precise measurements to provide **reliable results**. The discrepancy between a measurement’s estimated value and its actual value is referred to as accuracy.

If you deal with data, it’s critical to understand how to determine the quality of your **measurements** so that you can be confident your output is reliable and unbiased.

## Degree Of AccuracyÂ

Figure 1 illustrates the degree of accuracy i.e. half a unit on both sides.

we can see in figure 1 which shows our measurement in ones so the value between 6.5 and 7.4 will be considered as seven.

Accuracy is **frequently measured** by calculating the average value of several measurements. To ensure precise findings while working with a **collection of data**, it’s also crucial to determine the precision of those measures. The **degree of precision** indicates how well the various measurements match one another.

Finding the average deviation, which **computes the average** of the measurement discrepancies, allows you to assess accuracy. Data can be accurate without being exact, but for the best outcomes, measurements should be **accurate and precise.**

**Importance of Measuring Accuracy**

Measuring calculation accuracy is crucial while working in **data-driven sectors** like science to ensure accurate outcomes**. Professionals** may ensure that they are gathering comprehensive and detailed data by using accurate measures. The information these experts generate often might assist in validating or **establishing standards** that others in their field might use as a guide for many years.

To guarantee the long-term validity of their findings, these experts must gather precise** measurements**.

**Measurement of Accuracy and Precision**

Following are the steps to measure the accuracy and precision of the data. Figure 2 illustrates the example of high accuracy and low precision.

Figure 3 illustrates the example of high accuracy and high precision.

**Collection of Data**

Start by compiling all the information you have for the experiment or project. For a thorough **assessment of accuracy**, it’s critical to gather as **much data** as you can. It’s beneficial to electronically record the measurements when working with a lot of data utilizingÂ tools like spreadsheet software. You may identify the range of data you’ve collected by sorting the data values from **least to largest**.

**Average Value**

After gathering and **organizing your data**, you may calculate its average value, which can help you gauge its correctness. Add up all of your **data,** then divide it by the total number of measurements to get the average value. You can develop a formula in spreadsheet **software** that will determine this value for you. You might opt to manually calculate the measure using the following formula when dealing with tiny quantities of data:

\[ \textsf{Average Value} = \frac{\textsf{sum of data}}{\textsf{number of measurements}} \]

**Percentage Error**

By determining the percent error, you may also determine the accuracy of your measurements in **percentages**. This can be a useful tool for communicating your findings to someone who might not be familiar with the data’s **standard measurement**.

\[ \textsf{Percent error} = \frac{\textsf{accepted value}-\textsf{measured value}}{\textsf{accepted value}} \mathsf{\times 100} \]

**Absolute Deviations**

You might also want to know the **precision of your data** after determining the accuracy of your data since it can help you assess your measurements. Finding your **data’s average value** is the first step in calculating precision. You can get a collection of **absolute deviations** by taking each measurement out of the **average value** after you get it. How closely a measurement resembles the average is shown by its absolute deviation.

**absolute deviation = measured value – average value**

**Average Deviations**

You may compute the average deviation for the data, which demonstrates the precision, after computing the **absolute deviation** for each measurement. Add the absolute deviations for each measurement together, then divide by the total number of **measurements** to find the average deviation.

\[ \textsf{Average Value} = \frac{\textsf{sum of absolute deviations}}{\textsf{number of measurements}} \]

**Use of Approximations in Real Life**

Using rounded numbers to approximate **computation results** is known as anÂ approximation. We may use a**pproximation** to determine whether or not an answer to a computation is the correct size. Round the integers to simple numbers, often 1st or 2nd, or to the closest whole number to provide an approximation of the result of a computation. Then, using these **simple numbers**, calculate the **approximate solution.**

**Degree of Approximations in the Construction Industry**

The unit of payment and the item’s rate are the two factors taken into account when creating an estimate. The precision with which the values are estimated should increase as the rates rise. The measurements must be exactly** accurate**. if payments are made in units and the rates are high.

Where masonry is paid by cubic meter, **a few centimeters** added or subtracted to a wall’s height or length would not make much of a difference. On the other hand, the wall’s width and thickness need to be measured quite precisely. This is because a quarter- or **half-centimeters** might dramatically alter the **outcome**.

**Examples of Measuring the Degree of Accuracy**

**Example 1 **

The average value of this data is 10.02 when measuring the weight of a material and calculating distinct measurements of 10, 10, 2, 9, and 10.1 pounds. You’ve gotten a very accurate result if the real benchmark for this number is 10 pounds.

**Solution**

Average value = $\mathsf{\dfrac{(10 + 10.2 + 9.8 + 10.1) } {4}}$ = 10.02

**Example 2 **

If you gather data to gauge a climate’s average temperature and discover that it is 95.3 degrees but the recognized figure is 96.8 degrees, your data’s percent error is 1.5%. This indicates that your findings were within 1.5% of the allowed value.

**Solution**

Percent error =$\mathsf{\dfrac{(96.8-95.3) }{96.8}}$ x 100= 1.5%

### Example 3

Give the following to the nearest hundred:

a) 7.0149

b) 8.4739

c) 9.00692

### Solution

a)As we have to round off to the nearest hundred and the last digit is nine if it is greater than five so it will be 7.015 now the last digit is five and the previous number is odd so it will be 7.02.

b)As we have to round off to the nearest hundred and the last digit is nine so it is greater than five so it will be 8.474 now the last digit is four less than five so it will be 8.47.

c) As we have to round off till the nearest hundred and the last digit is two so it is less than five so it will be 9.0069 now the last digit is nine and it is greater than five so the number will be 9.007 last digit is seven which is greater then five so it will be 9.01.

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