Jeff Hosea : University of Surrey, Physics Dept, Level 1 Labs, Oct 2008

1. Level 1 Laboratories A Rough Summary of Key Error Formulae for samples of random data. For details see Physics Lab Handbook (section 4.5.2 to 4.5.4) 1 Jeff Hosea : University of Surrey, Physics Dept, Level 1 Labs, Oct 2008

2. Mean Standard Deviation  Frequency Quantity x (e.g. rebound height) Normal, or Gaussian, distribution – a “bell-shaped” curve 68.3% of area under curve 2 Jeff Hosea : University of Surrey, Physics Dept, Level 1 Labs, Oct 2008

3. Mean Standard Deviation  Frequency Quantity x (e.g. rebound height) Normal, or Gaussian, distribution – a “bell-shaped” curve 68.3% of area under curve In reality, only a finite amount of measurements can be made. If we then plotted a histogram, it would only approximate the true Normal Distribution. Nevertheless, we can still estimate the mean and standard deviation. 3 Jeff Hosea : University of Surrey, Physics Dept, Level 1 Labs, Oct 2008

4. Mean Standard Deviation  Frequency Quantity x (e.g. rebound height) Note : most simple calculators will provide and (often shown on calc. as “xn-1” ) Then one should quote the final result as : Where is called the “Standard Error in the Mean”, given by : Normal, or Gaussian, distribution – a “bell-shaped” curve 68.3% of area under curve 4 Jeff Hosea : University of Surrey, Physics Dept, Level 1 Labs, Oct 2008

5. Example calculation of , & Suppose we have a set of 10 measurements of nominally the same thing (e.g. bounce height): 64, 66, 68, 70, 72, 68, 72, 70, 71 and 70 cm • Mean • Variance (or Mean • Squared Deviation) (same as “xn-1” on Casio calculators) • Standard Deviation • Standard Error • (in the Mean) • Quote final result as Mean ± Standard Error : i.e. 5 Jeff Hosea : University of Surrey, Physics Dept, Level 1 Labs, Oct 2008