Unit 1: Matter & Measurement Section 4: Accuracy, Precision, and Error

Introduction On January 4, 2004, the Mars Exploration Rover Spirit landed on Mars. Each day of its mission, Spirit recorded measurements for analysis. In the chemistry laboratory, you must strive for accuracy and precision in your measurements.

Accuracy and Precision and Error Accuracy - how close a measurement comes to the actual or true value of whatever is measured. Precision - how close a series of measurements are to one another.

To evaluate the accuracy of a measurement, the measured value must be compared to the correct value. To evaluate the precision of a measurement, you must compare the values of two or more repeated measurements.

Accuracy and Precision The distribution of darts illustrates the difference between accuracy and precision. a) Good accuracy and good precision: The darts are close to the bull’s-eye and to one another. b) Poor accuracy and good precision: The darts are far from the bull’s-eye but close to one another. c) Poor accuracy and poor precision: The darts are far from the bull’s-eye and from one another.

Practice Problems Three students measure the volume of an object to be 10.4 mL, 10.5 mL, and 10.7 mL. The actual volume is 10.6 mL. Are the measurements accurate? Are the measurements precise? Yes! Yes!

2. Five students weigh a sample of metal. Here are their measurements: 2.486 g, 2.487 g, 2.487 g, 2.488 g, 2.486 g The actual weight of the metal is 2.600 g. Are the measurements accurate? Are the measurements precise? No! Yes!

3. Which set of measurements of a 2.00-g standard is the most precise? a) 2.00 g, 2.01 g, 1.98 g b) 2.10 g, 2.00 g, 2.20 g c) 2.02 g, 2.03 g, 2.04 g d) 1.50 g, 2.00 g, 2.50 g

experimental value – actual value Determining Error The actual (accepted) value is the correct value based on reliable references. The experimental value is the value measured in the lab. Percent error tells you how accurate your results are. % error = experimental value – actual value actual value X 100

% Error Example 1: Determine the % error if the measured temperature of a solution is 99.1˚C and the actual temperature is 100.0˚C % error = 99.1˚C – 100.0˚C x 100 100.0˚C = 0.9˚C x 100 100.0˚C = 0.9%

% Error Example 2 A technician experimentally determined the boiling point of octane to be 124.1˚C. The actual boiling point of octane is 125.7˚C. Calculate the percent error. Percent error = 124.1˚C – 125.7˚C x 100 125.7˚C = 1.6˚C x 100 125.7˚C = 1.27%

Just because a measuring device works, you cannot assume it is accurate. The scale below has not been properly zeroed, so the reading obtained for the person’s weight is inaccurate. The scale below has not been properly zeroed, so the reading obtained for the person’s weight is inaccurate. There is a difference between the person’s correct weight and the measured value. Calculating What is the percent error of a measured value of 114 lb if the person’s actual weight is 107 lb?