Solved Examples of Accuracy and Precision

Examples 1: A chemist measures the boiling point of water five times in a laboratory setting. The results are as follows: 99.8°C, 100.1°C, 100.0°C, 99.9°C, and 100.2°C. Knowing that the actual boiling point of water at sea level is exactly 100°C, calculate the accuracy and describe the precision of the measurements.

Solution :

• Accuracy: The average of the measurements is calculated by adding all the results together and dividing by the number of measurements:

Average = (99.8 + 100.1 + 100.0 + 99.9 + 100.2) /5​ = 100.0°C

This average exactly matches the known boiling point of water, showing that the measurements are highly accurate. Accuracy here reflects how close the measurements are to the true or accepted value.

• Precision: Precision relates to the repeatability of measurements and how close the series of results are to each other. The range of measurements from 99.8°C to 100.2°C shows very tight clustering around the average. This indicates that the chemist’s measurements are consistently precise..

Examples 2: An archer practices by shooting arrows at a target, aiming for the bullseye. The scores recorded are 9, 10, 10, 9, 10. If 10 is the bullseye, assess the accuracy and precision of the archer’s shots.

Solution:

• Accuracy: Most of the archer’s shots hit the bullseye or very close to it, showing a high level of accuracy. Accuracy in this context is how close each shot is to the intended target, which is the bullseye.
• Precision: The shots consistently hit near or at the same spot (bullseye and just around it), indicating a high degree of precision. Precision here demonstrates the archer’s ability to deliver repeatable performance over multiple attempts.

Examples 3: A medical thermometer is calibrated to verify its accuracy at a known temperature of 37.0°C. It records the following temperatures: 36.8°C, 36.9°C, 37.1°C, 37.0°C, and 37.1°C. Evaluate the thermometer’s accuracy and precision based on these readings.

Solution:

Accuracy: The average reading is calculated as follows:

(36.8 + 36.9 + 37.1 + 37.0 + 37.1​) /5​ = 37.0°C

The average matches the expected temperature. This shows that the thermometer is accurate in measuring temperature.

Precision: The measurements are all within 0.3°C of each other, indicating a high level of precision. This demonstrates the thermometer’s ability to provide consistent results under the same conditions.

Examples 4: A machine in a factory is set to cut sheets of metal to a precise length of 200 cm. After production, five sheets are measured and found to be 200.1 cm, 199.8 cm, 200.0 cm, 200.2 cm, and 199.9 cm. Determine the machine’s accuracy and precision from these measurements.

Solution:

Accuracy: To find the average length:

(200.1+199.8+200.0+200.2+199.9​) /5​ =200.0cm

The average length exactly meets the specified length, demonstrating the machine’s accuracy in cutting the metal sheets.

Precision: The spread between the measurements is minimal, only varying by 0.4 cm, which signifies a high precision. This consistency shows that the machine can reliably reproduce the same length in its cuts.

Accuracy means how close a measurement comes to the true value while precision refers to how consistently one can repeat a measurement. Every measurement contains some uncertainty in them. It may be due to limitations in measurement tools, observer variation, or environmental factors. This affects both the accuracy and precision of measurements. In this article, we are going to learn about accuracy and precision in detail, along with their examples and differences.