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UNIT 2.3 • Data Analysis
A C C U R A C Y & P R E C I S I O N Idea 1: Measurements (3.25 cm) ___________________________________________ numbers (3.14159265).
Measurements represent an action by someone with ______________________________ Measurements have built-in uncertainty; no measurement ______________________ Measurements have ____________________
Idea 2: The uncertainty in a measurement needs to be communicated.
Definitions: accuracy – how close a measurement is to _______________________________ precision – how close a measurement is to _______________________________
Precision versus Accuracy: Look at each target below and decide whether the situation is accurate, precise, both, or neither: (Note: it is “accepted” that the bull’s eye is the place everyone aims for.)
Accurate?: Yes / No Precise?: Yes / No
Accurate?: Yes / No Precise?: Yes / No
Accurate?: Yes / No Precise?: Yes / No
_________________________________ measures Precision
___________________________________ measures Accuracy
Error range = Average ± range of values
Precision Problems: Several lab groups measure the density of aluminum. Here is their data: Team 1 Team 2 Team 3 Team 4 Team 5 Team 6 Team 7 2.65 g/cm^3 2.75 g/cm^3 2.80 g/cm^3 2.77 g/cm^3 2.60 g/cm^3 2.65 g/cm^3 2.68 g/cm^3
What is the average density? ________g/cm^3
Subtract the highest value from the lowest value: _________
Divide this number by 2: _______
The precision of the measurement can be shown as ________±_____ g/cm^3.
This is called __________
Team 1 Team 2 Team 3 Team 4 Team 5 Team 6 Team 7 2.65 g/cm
3 2.73 g/cm
3 2.71 g/cm
3 2.74 g/cm
3 2.65 g/cm
3 2.64 g/cm
3 2.78 g/cm
3
Find the error range for the new samples above.
Is this more precise, less precise, or the same precision as the previous set of data?
Accuracy Problems:
% error =
actual value experimental value
actual value
x 100
- Working in the laboratory, a student find the density of a piece of pure aluminum to be 2. g/cm^3. The accepted value for the density of aluminum is 2.699 g/cm^3. What is the student's percent error?
- A student experimentally determines the specific heat of water to be 4.29 J/g x Co. He then looks up the specific heat of water on a reference table and finds that it is 4.18 J/g x Co. What is the percent error?
- A student takes an object with an accepted mass of 200.00 grams and masses it on her own balance. She records the mass of the object as 196.5 g. What is her percent error?
- Often, with accuracy we are concentrating on one measurement. However, we can also look at a collection of measurements and simply take the average. Does this target represent someone who is accurate? _____ Precise? ____
Team 1 Team 2 Team 3 Team 4 Team 5 Team 6 Team 7 2.65 g/cm
3 2.73 g/cm
3 2.71 g/cm
3 2.74 g/cm
3 2.65 g/cm
3 2.64 g/cm
3 2.78 g/cm
3
Find the error range for the new samples above. 2.70 ±±±± 0.07 g/cm^3
Is this more precise, less precise, or the same precision as the previous set of data? More precise, because the range of values is smaller than above
Accuracy Problems:
% error = |
actual value experimental value actual value
| x 100
- Working in the laboratory, a student find the density of a piece of pure aluminum to be 2. g/cm^3. The accepted value for the density of aluminum is 2.699 g/cm^3. What is the student's percent error? Accepted = actual = 2.699 g/cm^3
Working in lab = experimental = 2.85 g/cm^3
- A student experimentally determines the specific heat of water to be 4.29 J/g x Co. He then looks up the specific heat of water on a reference table and finds that it is 4.18 J/g x Co. What is the percent error? Reference table = actual = 4.18 J/g x Co
Experimentally determines = experimental = 4.29 J/g x Co
- A student takes an object with an accepted mass of 200.00 grams and masses it on her own balance. She records the mass of the object as 196.5 g. What is her percent error? Accepted = actual = 200.00 g
Records the mass = experimental = 196.5 g
- Often, with accuracy we are concentrating on one measurement. However, we can also look at a collection of measurements and simply take the average. Does this target represent someone who is accurate? Yes, because the average of these points is exactly in the middle of the bulls-eye. Precise? No, they are not consistent in the least.
For Percent Error: Actual value is the “correct” measurement. It usually comes from a reference book, textbook, the internet, or a known standard. Experimental value is what is measured in the experiment, either by the student or by a scientist
