Accuracy and Precision Introduction Scientists use many skills as they investigate the world around them. They make observations by gathering information with their senses. Some observations are simple. For example, a simple observation would be figuring out the color or texture of an object. However, if scientists want to know more about a substance, they may need to take measurements. Measurement is perhaps one of the most fundamental concepts in science. Without the ability to measure, it would be difficult for scientists to conduct experiments or form theories. Not only is measurement important in science and the chemical industry, it is also essential in farming, engineering, construction, manufacturing, commerce, and numerous other occupations and activities. The word measurement comes from the Greek word metron, which means limited proportion. Measurement is a technique in which properties of an object are determined by comparing them to a standard. Measurements require tools and provide scientists with a quantity. A quantity describes how much of something there is or how many there are. A good example of measurement is using a ruler to find the length of an object. The object is whatever you are measuring, the property you are trying to determine is the object s length, and the standard you are comparing the object s length to is the ruler. Essential Question: How is accuracy and precision used in science and engineering? Explain the importance. Equipment/Materials thermometer micropipet 50 ml Beaker 250 ml Beaker Top loading balance 10 ml Graduated cylinder distilled water volumetric Pipet Safety Always wear goggles in the lab. Read labels carefully and always handle substances with care. Wash hands at the end of the lab. Pre-Lab 1. If choosing between measuring a tsp of vanilla with a 1 cup, ½ cup, or a TBSP which instrument would be best to use? Explain your reasoning. 2. If choosing between measuring 1 ml with a 1000-mL beaker, 50-mL beaker, or a graduated cylinder, which instrument would allow you to measure the 1 ml most accurately and/or precisely? Explain your reasoning. 3. Examine the volume measuring instruments at your station (50-mL beaker, 10-mL graduated cylinder, a 1 ml volumetric pipette, and a micro-pipet). What difference in terms of measurement do you notice? 4. Considering the volume measuring instruments, what piece of equipment can measure 1-mL to the most decimal places? Defining accuracy as the closeness of a measurement to the true or accepted value which instrument would you expect to measure most accurately and why? 5. Examine the balances at the lab station, which balance records the most decimal places? Why is it important to record all of the numbers displayed on the individual balance? Page 1 of 6
Procedure Place about 100 ml of distilled water in a 250 ml beaker, called the supply beaker. Allow the water to come to room temperature. Measure the temperature of the water and record it on the data table. Use this water for all of the measurements below. Follow this procedure for BOTH the toploading and the analytical balance. Record all measurements to the number of decimal places allowed by the measuring device. Beaker 2. Pour 1 ml of water from the supply beaker in to the 50 ml beaker, using only the markings available. Put the water from the 50 ml beaker into the tared weigh boat. Record the mass of water added to the weigh boat. Tare. 3. Measure another ml of water into the 50 ml beaker. Add this ml of water to the weigh boat in the same manner as above. Record the mass of water added to the weigh boat. Tare. 4. Repeat step two one more time. Record the mass of water added to the weigh boat. 5. Have the teacher check the recorded value for the volume. Graduated cylinder 2. Using the 10 ml graduated cylinder as the measuring instrument for volume, add 1 ml of water from the supply beaker to the tared weigh boat. Record the mass of water added to the weigh boat. Tare. 3. Measure another 1 ml of water using the graduated cylinder and add to the weigh boat. Record the mass of water added to the weigh boat. Tare. 4. Repeat step two one more time. Record the mass of water added to the weigh boat. 5. Consider that the volume recorded should reflect one estimated digit past the smallest measurement on the measuring instrument. Pipet 2. Using the volumetric pipet as the measuring instrument for volume, add 1 ml of water from the supply beaker to the tared weigh boat. Record the mass of water added to the weigh boat. Tare. 3. Add another 1 ml of water to the weigh boat. Record the mass of water added to the weigh boat. Tare. 4. Add another 1 ml of water to the weigh boat. Record the mass of water added to the weigh boat. 5. Note the certainty of measurement for the volumetric pipet. Micro-pipet 2. Using the micro-pipet as the measuring instrument for volume, add 1 ml of water from the supply beaker to the weigh boat. Record the mass of water added to the weigh boat. Tare. 3. Add another 1 ml of water to the weigh boat. Record the mass of water added to the weigh boat. Tare. 4. Add another 1 ml of water to the weigh boat. Record the mass of water added to the weigh boat. 5. Verify the measurement to have one estimated digit beyond what the micro-pipet can measure. Page 2 of 6
Data Temperature of water oc Equipment used volume mass Name Accepted density of water at this temp. Volume (ml) H 2 O Mass (g) Density (g/ml) Average Density (g/ml) Beaker Graduated Cylinder Pipet Micro-pipet Beaker Graduated Cylinder Pipet Micro-pipet Page 3 of 6
Data Analysis Calculations/Results 1. Calculate the % error (accuracy) for each average density value. % error = accepted value your calculated average x 100 accepted value % ERROR for: Top-loading Analytical Beaker % % Graduated Cylinder % % Pipet % % Micro-pipet % % Accepted Values for the Density of Water from Modern Chemistry Temperature Density Temperature Density C g/ml C g/ml 0 0.99984 23 0.99753 2 0.99994 24 0.99730 3.98 (max) 0.999973 26 0.99678 4 0.99997 30 0.99565 6 0.99994 40 0.99222 8 0.99985 50 0.98804 10 0.99970 60 0.98320 14 0.99924 70 0.97777 16 0.99894 80 0.97179 20 0.99820 90 0.96531 21 0.99799 100 0.95836 22 0.99770 Questions Part 1 1. How is accuracy defined? 2. Examine the percent error equation, what is the measured value being compared to in the percent error equation? 3. Which method of determining density was most accurate? Which was least accurate? Explain how percent error is used to indicate accuracy. 4. Explain how an instrument of measurement can influence how accurately a measurement can be made. Create an analogy to help explain the relationship between accuracy and a measuring instrument. Part 2 5. How is precision defined? 6. Examine the equation below. What is each individual trial being compared to in the equation? standard deviation = (X avg X) 2 n 1 where X = density for each individual trial X avg = average density n = number of trials Page 4 of 6
7. Working as a group, complete one calculation for standard deviation. When taking the square root, how is the answer reported? 8. By inspection, which method of determining density was most precise? How do you know? How does this result compare to the calculated standard deviation? Part 3 9. James has been asked to measure the diameter of a lug nut for a 2010 Mini Cooper wheel. Choose the correct piece of equipment James would use and explain why. a. b. c. 10. Boiling temperature ( C ) Test Group 1 Group 2 Group 3 Group 4 1 95.0 99.0 99.0 102.5 2 91.0 100.0 100.0 100.5 3 90.5 101.0 99.5 101.0 Average a. What group has the average measured value closest to the accepted value of 100 C at 1.0 atmosphere (atm) for water? b. What group has the most accurate result? c. Which group has the most precise readings? d. Why would group 1 not be happy with their results? e. How could group 1 test the reasons for their results? Page 5 of 6
Elaborate When does being accurate really matter? Measuring out orange Kool-aid to make a cool refreshing drink. Weighing an adult man Measuring air temperature Timing a 100 m breast stroke swimming race Weighing a premature baby Training for an 800 m running race. Weighing out aspirin to make it into a 500 mg tablet You are on a building site and are asked to measure out some sand, cement and gravel, which will then be mixed together to make some concrete. Building an Olympic swimming pool. You need to measure the length of the pool which is 50 m. Analysis of water to see what pollutants are present. You will need to measure a known volume of water in order to carry out the analysis. 1. Read the situations above and sort them into two groups. The first group requires accurate measurements and the second group can have rougher estimations. Create a table to present answers. 2. Decide for each situation if more than one variable needs to be measured accurately. Record results in a table. An example is provided. Situation Variable 1 Variable 2 100 m breast stroke Timing 100 m length Page 6 of 6