11. Statistical Analysis

Describe and give examples of random uncertainties and systematic errors

Random Uncertainty- Decreases the precision of the instrument in use.

EXAMPLE: Grad. Cylinder only measures to the nearest mL (the error is +/- 0.5 mL because the true value can be anywhere between those two tick marks)

Systematic Error- Results in a decreased accuracy. Usually in one direction (greater or smaller). Caused by either instruments or the way something is measured.

EXAMPLE: Scale can be calibrated wrong or when reading from a graduated cylinder, you read from the top of the meniscus

Distinguish between precision and accuracy

Precision- Measurement of how close measurements are to each other (+/- value)

Accuracy- Measurement of how close measurements are to an accepted value

Describe how the effects of random uncertainties may be reduced

Random uncertainties may be reduced by repeating the experiment (multiple trials)

State random uncertainty as an uncertainty range

Random Uncertainty is a range of values (ex. 25.0 +/- 0.1 is a range b/w 24.9 and 25.1

State the results of calculations to the appropriate number of significant figures

3 Rules of Sig. Figs that I Stole From My Physics Teacher

1. Any non-zero integer is significant

2. All Final Zeroes after the decimal place are significant (like 24.60)

3. All Zeroes between Sig figs are significant (like 35.6009 or 1,000,001)

When Adding or Subracting Sig Figs- Use the smallest decimel place

  616.1

+ 22.52   .

  638.62 = 638.6

When Multiplying or Dividing Sig Figs- Use the smallest number of sig figs

      220

  X 881

193820  =  194000

State uncertainties as absolute and percentage uncertainties AND Determine the uncertainties in results

Absolute Uncertainties have a defined number (1.55 +/- 0.40)

Percent Uncertainties can be calculated using the equation:

Absolute Uncertainty  x  100 = %

          Value

When adding or subtracting uncertainty, add the absolute uncertainty

When multiplying or dividing uncertainty, add the percentage uncertainty

When raising to a power, multiply the percentage uncertainty

Sketch graphs to represent dependences and interpret graph behavior

Construct graphs from experimental data

Draw best-fit lines through data points on a graph

Determine the values of physical quantities from graphs

Author’s Note: There’s no real trick to teaching this. It’s really something you either learn in math or pick up through experience. I will try and find practice problems and post them if I can find them