# Topic 11: Measurement and Data Processing

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Topic 11: Measurement and Data Processing
IB Core Objective Distinguish between precision and accuracy. Distinguish: Give the differences between two or more different items. (Obj. 2)

11.1.2 Distinguish between precision and accuracy.
Accuracy: How close you are to the true value Precision: How reproducible your measurements are.

11.1.2 Distinguish between precision and accuracy.
Random Systematic (Not precise not accurate) (precise but not accurate) Good reading (precise and accurate)

IB Core Objective Describe and give examples of random uncertainties and systematic errors. Describe: Give a detailed account. (Obj. 2)

11.1.1 Describe and give examples of random uncertainties and systematic errors.
Types of error: Random error: Is caused by measurement estimation when reading equipment. If the measurements are inconsistent then the lab technique is poor. Systematic error: Is caused by instrumentation error. Technique is good but equipment is faulty or un-calibrated. This will result in consistent but wrong readings.

11.1.1 Describe and give examples of random uncertainties and systematic errors.
A random uncertainty can arise from inadequacies or limitations in the instrument, such as pinpointing the reading of a burette or graduated cylinder. Examples of a systematic error can be from reading a burette from the wrong direction, reading the top of the meniscus instead of the bottom, or using equipment that is not well calibrated.

IB Core Objective Describe how the effects of random uncertainties may be reduced. Describe: Give a detailed account. (Obj. 2)

Describe how the effects of random uncertainties may be reduced. We will be learning more about this when we do labs. This is also why we ask you to collect data several times (3-5 times) for an experiment. Repeating should increase the precision of the final result since random variations can be statistically cancelled out (or dropped if it is way off).

IB Core Objective State random uncertainty as an uncertainty range (±) State: Give a specific name, value, or other brief answer without explanation or calculation. (Obj. 1)

11.1.4 State random uncertainty as an uncertainty range (±)
Absolute uncertainty: Is the measurement you are guessing Ex: cm3 pipette has an absolute uncertainty of ±0.1cm3 100cm3 beaker has an absolute uncertainty of ±1cm3

11.1.4 State random uncertainty as an uncertainty range (±)
Instruments may have the tolerance (i.e. uncertainty) clearly labeled. If the tolerance is not labeled on the instrument, you will have to determine the uncertainty yourself. A digital scale may bounce around on the last digit (i.e. between and 3.760). The uncertainty would be ± If it bounces around by five on the last digit, then it would be ± .005. We will practice this in labs.

IB Core Objective State the results of calculations to the appropriate number of significant figures State: Give a specific name, value, or other brief answer without explanation or calculation. (Obj. 1)

11.1.5 State the results of calculations to the appropriate number of significant figures
Estimating the number Bathroom scale Balance Grape fruit kg kg Grape fruit kg kg Certain digits: The numbers we know Uncertain digits: The estimated number. The bolded numbers represent the guessed digit. Significant Figures The number of figures known + one guessed figure. The bathroom scale has: 2 sig. Figs. The balance has: 4 sig. Figs

11.1.5 State the results of calculations to the appropriate number of significant figures
Leading Zeros (Zeros to the Left of the decimal place) Don’t count! They are just place holders. Value # of sig figs Sci. notation 0.0056 g 0.01

11.1.5 State the results of calculations to the appropriate number of significant figures
Trailing Zeros (Zeros to the Right End of the number) Only count when the number contains a decimal place. Value Sig figs 1.00 300. 300.0 1000 6.02 x 1023

11.1.5 State the results of calculations to the appropriate number of significant figures
Addition/Subtraction: When adding and subtracting data, use the measurement with the least number of decimal places. Value # of d.p. Answer 5.5 – 0.13 5.12 x 1.5 –

11.1.5 State the results of calculations to the appropriate number of significant figures.
Multiplication/ Division When multiplying and dividing, your answer should have the number of sig. figs as the one with the least number of sig figs. Value # of sig figs Answer 4.56 x 1.4 .50 x 100 25.0 ÷ 5.00 1.0 x 102 ÷ 5

IB Core Objective State uncertainties as absolute and percentage uncertainties. State: Give a specific name, value, or other brief answer without explanation or calculation. (Obj. 1)

11.2.1 State uncertainties as absolute and percentage uncertainties.
Percent uncertainty: Absolute uncertainty x 100 Amount used If we take a 30cm3 sample in the 100cm3 beaker (with a ± 1 uncertainty) what is the % uncertainty? % uncertainty = 1/30 x 100  3.33% If we take a 90cm3 sample in the 100cm3 beaker what is the % uncertainty? % uncertainty = 1/90 x 100  1.11% This is why taking small samples with a large beaker is not a good idea! Use the proper tool!!

IB Core Objective 11.2.2 Determine the uncertainties in results.
Determine: Find the only possible answer. (Obj. 3)

11.2.2 Determine the uncertainties in results.
Adding/ Subtracting uncertainties Just add the uncertainties of each piece of equipment Add the two volumes from the previous example 30 (±1) +90(±1) 120 (±2)  (So range is )cm3. % uncertainty = 2 ÷ 120 x 100  0.83%

11.2.2 Determine the uncertainties in results.
Multiply/Dividing uncertainties Each measurement must have the % uncertainty calculated. The % uncertainties are then added The final % uncertainty is then used to re-calculate the final absolute uncertainty. Scale = 5.000g (±0.001) Pipette = 50.00cm3 (±0.01) Graduated cylinder = 25.0cm3 (±0.05)

11.2.2 Determine the uncertainties in results.
Answer 0.001 ÷ x 100 = 0.02% 0.01 ÷ x 100 = 0.02% 0.05 ÷ 25.0 x 100 = 0.2% Total percentage = 0.24% If the molar mass in the end was determined to be 64.0 g/mol, then x 64.0 = , So final answer is 64.0 g/mol ± 0.2g