# Accurate vs Precise

Accurate vs Precise
Go back to  'Measurement'

Most of us like shooting arrows to the dartboard, targetting at the bull's eye, that is the center of the dartboard.

The closer the darts land to the bull's eye, the more accurate our aim will be. What is meant by precision then? When can you consider any measure precise?

Let's have a look!

Explore the simulation below and try to shoot the arrows towards the bull's eye.

Hope you enjoyed it!

Let's learn about accurate vs precise examples, accurate and precise definition, and accuracy and precision difference in detail.

Check out the interesting examples to know more about the lesson and try your hand at solving a few interactive questions at the end of the page, for quick revision.

## Lesson Plan

 1 What Is Meant by Accurate and Precise? 2 Thinking out of the Box! 3 Important Notes on Accurate vs Precise 4 Solved Examples on Accurate vs Precise 5 Interactive Questions on Accurate vs Precise

## What Is Meant by Accurate and Precise?

Our day-to-day activities are just incomplete without measurements.

From medical check ups to controlling temperature of appliances to sports and even cooking, all require measurements in some way or the other.

Measurements require tools, either conventional or unconventional.

Also, different people may get different results using the same instrument.

That further leads to measurements of any value being either accurate or precise.

Let's consider common accurate vs precise examples.

Let’s consider the value of pi, i.e, 3.1459265359

3.14 is a number for representing the value of pi, which is not precise but accurate, based on closeness. No other number with three digits can get closer to the target.

Accuracy of a number is given by the number of digits to the right of the decimal.

Precision is the maximum number of digits to the right of the decimal.

Answers may vary as two people might be considering different values.

Thus, accuracy and precision are two important factors to be considered while taking measurements. Both reflect how close a measurement is to a known or accepted value.

If you weigh a given substance five times and get 1.2 lbs each time, then your measurement is very precise but not necessarily accurate.

It's because you are getting values that are so close to each other.

### Accurate and Precise Definition

Accurate is defined as the closeness of a value to its true value, such as the closeness of an arrow to the bull's eye at the center.

Accurate is correct, that is the bull's eye.

Precise is defined as the repeatability of the values of a measurement, such as the closeness of other arrows to the first one.

Precise is repeating, that is hitting the same spot, but that may not even be the correct spot.

Let's have a look!

Think Tank
• Determine the measurements as accurate or precise in the following cases:
1. When the darts are neither close to the bulls eye, nor close to each other.
2. When all of the darts land very close together, but far from the bulls eye.
3. When the darts land close to the bulls eye and close together.
• If you are playing football and you always hit the right goal post instead of scoring, then would you consider it as accurate or precise?

## What Is the Difference Between Accurate and Precise?

Let's explore the difference between the two.

### Accuracy and Precision Difference

Accuracy Precision

The degree of correctness to the true or exact value.

The degree of exactness to the values obtained each time.

The closeness of the measured value to a standard or true value.

The closeness of two or more measured values, to each other.

Single measurement Multiple measurements
For something to be accurate consistently, it must be precise. Precision is independent of accuracy.

Important Notes
1. Accuracy is how close a value is to its true/actual value.
2. Precision is comformity or repeatability of values.
3. Percent error(the ratio of the error to the actual value multiplied by 100) is used to assess the accuracy or precision of a measurement value.
4. Accurate vs Precise Formula

Accuracy = (True positives + True Negatives)/ (True positives + True negatives + False positives + False negatives)

Precision = True positives/ (True positives + False positives)

## Solved Examples

Here are a few accurate vs precise examples. Let's have a look!

 Example 1

Jack, a snack foods manufacturer, produces bags of potato chips, each measuring 11 oz.

He tests the weight of the bags using a scale that measures the bags.

There is little variation in the measurements: 12.2 oz, 12.33 oz, and 12.13 oz, for three samples.

What does this tell about the scale?

Solution

Three samples = 12.2 oz, 12.33 oz, and 12.13 oz.

There is little variation in the measurements.

The scale measures the bags precisely, but not accurately.

 $$\therefore$$ The measurements of the three samples are precise.
 Example 2

Masurement of the mass of a 5 lbs standard sample.

(i) Values - 4.5, 4.6, 4.5, and 4.7 lbs

(ii) Values - 4.8, 5.1, 5.0, and 4.9 lbs

Solution

(i) Precise (there is little variation in the measurements)

(ii) Accurate (close to the true value)

 $$\therefore$$ (i) Precise (ii) Accurate
 Example 3

Annie has to check which set of data is more precise?

Look at the two given sets and help her.

Set A: 33.49, 33.47, 33.29, 33.40, 33.28

Set B: 16.80, 16.81, 16.90, 16.78, 16.85

Solution

In order to check which sets of data is more precise:

1. Select the lowest vale and the highest value from each set
2. Subtract

Set A = 33.49 - 33.28 = 0.21

Set B = 16.90 - 16.78 = 0.12

Since sample B has the lowest range, it's more precise.

 $$\therefore$$ Data in set B is more precise.

## Interactive Questions

Here are a few activities for you to practice.

## Let's Summarize

The mini-lesson targeted in the fascinating concept of accurate vs precise. The math journey around cardinal numbers starts with what a student already knows, and goes on to creatively crafting a fresh concept in the young minds. Done in a way that not only it is relatable and easy to grasp, but also will stay with them forever. Here lies the magic with Cuemath.

At Cuemath, our team of math experts is dedicated to making learning fun for our favorite readers, the students!

Through an interactive and engaging learning-teaching-learning approach, the teachers explore all angles of a topic.

Be it worksheets, online classes, doubt sessions, or any other form of relation, it’s the logical thinking and smart learning approach that we at Cuemath believe in.

## 1. Can measurement be both accurate and precise?

Measurements can be both accurate and precise, accurate but not precise, precise but not accurate, or neither, depending on the values.

## 2. Does precise mean exact?

Precise can be referred to as the exact value.

## 3. How can results be precise but not accurate?

Precision refers to how close measurements of the same item are to each other.

Precision is independent of accuracy.

That means it is possible to be very precise but not very accurate, and it is also possible to be accurate without being precise.

More Important Topics
Numbers
Algebra
Geometry
Measurement
Money
Data
Trigonometry
Calculus