4) Average, standard deviation, and uncertainty. A student is trying to determine the density of a (post 1982) penny. She measures the mass of 10 pennies individually. Her lab partner then measures the volume of the ten pennies. She (gently) drops the stack of coins into a prefilled 25 mL graduated cylinder (0.2 mL graduations), recording the volume before and after the addition of the pennies. Uncertainties (random): Balance: ±10 mg Graduated cylinder: ±0.15 mL Data: Change in volume (10 pennies): V₁: 10.0 mL V 13.4 mL Reported masses: 1. 2.49 g 2. 2.50 g 3. 2.48 g 4. 2.49 g 5. 2.51 g 6. 2.51 g 7. 2.49 g 8. 2.52 g 9. 2.49 g 10. 2.50 g
4) Average, standard deviation, and uncertainty. A student is trying to determine the density of a (post 1982) penny. She measures the mass of 10 pennies individually. Her lab partner then measures the volume of the ten pennies. She (gently) drops the stack of coins into a prefilled 25 mL graduated cylinder (0.2 mL graduations), recording the volume before and after the addition of the pennies. Uncertainties (random): Balance: ±10 mg Graduated cylinder: ±0.15 mL Data: Change in volume (10 pennies): V₁: 10.0 mL V 13.4 mL Reported masses: 1. 2.49 g 2. 2.50 g 3. 2.48 g 4. 2.49 g 5. 2.51 g 6. 2.51 g 7. 2.49 g 8. 2.52 g 9. 2.49 g 10. 2.50 g
Chapter2: Basic Statistical Analysis With Excel
Section: Chapter Questions
Problem 4P
Related questions
Question
- What is the average mass of the 10 pennies? Report your value with correct significant figures.
- What is the error (uncertainty) associated with each mass measurement due to the equipment?
- What is the uncertainty associated with the average value? Note that the uncertainty of the balance will propagate throughout the calculation.
- What is the standard deviation of the 10 mass measurements?
- Explain the difference between the propagated uncertainty and the standard deviation. Which number would you use to describe the uncertainty in the measurement?
- Calculate the total mass of the pennies with associated uncertainty.
- Calculate the average density of a penny based on these data. Propagate the uncertainty values for both mass and volume in your calculations.
Transcribed Image Text:4) Average, standard deviation, and uncertainty. A student is trying to determine the density
of a (post 1982) penny. She measures the mass of 10 pennies individually. Her lab
partner then measures the volume of the ten pennies. She (gently) drops the stack of
coins into a prefilled 25 mL graduated cylinder (0.2 mL graduations), recording the
volume before and after the addition of the pennies.
Uncertainties (random):
Balance: ±10 mg
Graduated cylinder: ±0.15 mL
Data:
Change in volume (10 pennies):
V₁: 10.0 mL
V 13.4 mL
Reported masses:
1. 2.49 g
2. 2.50 g
3. 2.48 g
4. 2.49 g
5. 2.51 g
6. 2.51 g
7. 2.49 g
8. 2.52 g
9. 2.49 g
10. 2.50 g
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