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Precision and Accuracy

In order to get the most reliable results in a scientific inquiry, it is important to minimize bias and error, as well as to be precise and accurate in the collection of data. Both accuracy and precision have to do with how close a measurement is to its actual or true value.

What is the difference between “Precision” and “Accuracy”?

In everyday life, students may use the terms “precision” and “accuracy” interchangeably, but they have different meanings in math, science and experimental inquiry.they 

Accuracy

Accuracy refers to how close a measured value is to the actual (‘true’) value. For example, if you were to weigh a standard 100g weight on a scale, an accurate reading for that weight would be as close as possible to 100g. If you got a reading of 105g, then you would say that you were not getting an accurate reading (and your scale would need calibrating).

But what if you don’t know what the “true” value for something is? You still want to be able to take measurements that are as true as possible. Certain devices and tools allow you to be more accurate than others. For example, let’s say that you had two groups of students measuring the width of a tomato plant stem. One group used plastic rulers that only measured to the millimeter (mm). The students had to determine whether they thought the reading was closer to 3 or 4 mm (see below). Another group of students used Vernier calipers to take the measurements. They were able to measure to a tenth of a millimeter. If several measurements are made with a more precise instrument, such as calipers, then the average value can be considered a more accurate value than the one taken with a ruler.




Plastic Ruler - Less Accurate
tomato stem

Student responses: 3mm, 4mm, 3mm, 4mm

Vernier Calipers - More Accurate
tomato stem

Student responses: 3.5mm, 3.3mm, 3.4mm, 3.5mm



Precision

Precision refers to how close measured values are to each other. For example, one group of students (Group A) counted the number of tomatoes on their tomato plant, while another group of students (Group B) did the same for the tomatoes on their tomato plant.



Group A
tomato plant

How many tomatoes are on the plant?

Student responses: 37, 36, 37, 36, 37, 36

Group B
tomato plant

How many tomatoes are on the plant?

Student responses: 35, 38, 31, 40, 32, 37


Notice that the all of the values for Group A are very similar (either 36 or 37). The data would be considered to be very precise. On the other hand, the values for Group B show a much larger range (between 31 and 40). These measurements are not precise.


Precise and Accurate

It is possible to be accurate without being precise and precise without being accurate.



targetwith marks clustered around centre

Accuracy = high
Precision = high

target with marks clustered far from centre

Accuracy = low
Precision = high

target with marks spread out around centre

Accuracy = high
Precision = low

target with marks spread out far from centre

Accuracy = low
Precision = low


Students should always strive to make measurements that are BOTH accurate and precise.

For example, two sets of data were collected about the surface area of tomato plant leaves.



Accurate AND Precise
tomato leaf

Student responses: 53 cm2, 52 cm2, 53 cm2, 53 cm2

Values are close to each other and close to the average

NOT Accurate and NOT Precise
tomato leaf

Student responses: 47 cm2, 52 cm2, 59 cm2, 56 cm2

Values are not close to each other and some not close to the average



Precision and Accuracy in Tomatosphere™

Accuracy & Precision Hints:

To remember which is which, think:
Accuracy = Close to Correct
Precision = Repeatable

In the Seed Investigation, students are encouraged to make both precise and accurate measurements of seed germination. This primarily includes recording precise and accurate data for when the seeds germinate (both seed leaves are up and open). For example, if multiple students count the number of seeds they see germinated on a given day, they should each count the same number of seedlings. In further inquiries with the growing tomato plants, students may measure tomato plants’ height, dry mass, surface area of leaves, width of stems, etc.

Guided Practice

Exercise 1

Have students read and answer the following questions.

  1. Look at the measurements from the following two groups of students. Which group has the more accurate measurements for the height of the 50 cm plant?
    Group A: 49.7 cm, 50.0 cm, 49.8 cm, 50.1 cm, 50.2 cm
    Group B: 52.1 cm, 52.0 cm, 52.1 cm, 51.9 cm, 52.0 cm
  2. Look at the measurements from the following two groups of students. Which group has the more precise measurements for the height of the 50 cm plant?
    Group A: 49.9 cm, 50.0 cm, 49.8 cm, 50.1 cm, 50.2 cm
    Group B: 52.1 cm, 52.0 cm, 52.1 cm, 51.9 cm, 52.0 cm
  3. Look at the following measurements of soil pH from one pot. Are they precise? Explain.
    7.0, 5.2, 8.1, 6.3, 7.8

Exercise 2

In their own words, have student define the terms “precision” and “accuracy.”

Exercise 3

Have students identify a real-life example of a situation when precision is important. Have them also identify a situation when accuracy is important.

Exercise 4

Have the students create their own analogy, such as the bullseye analogy used on many websites, to explain the difference between accuracy and precision.

Answers

  1. Calculate the averages for each group. Group A has an average of 49.82 and Group B has an average of 52. Since the average of Group A is closer to 50 cm than the average of Group B, the values for Group A are more accurate.
  2. The values for Group B are closer to each other (smaller range) than the values for Group A; therefore Group B has more precise measurements, even though they are not as accurate.
  3. No, they are not. The range is from 5.2 to 8.1, which is a big difference on the pH scale for soil taken from one pot.

Additional Resources