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

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

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

Frequency Quantity x (e.g. rebound height) Mean Normal, or Gaussian, distribution – a “bell-shaped” curve Standard Deviation  68.3% of area under curve Jeff Hosea : University of Surrey, Physics Dept, Level 1 Labs, Oct 2008 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 : 4

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 (same as “x  n-1 ” on Casio calculators) Standard Error (in the Mean) Mean Standard Deviation Quote final result as Mean ± Standard Error : i.e. 5 Jeff Hosea : University of Surrey, Physics Dept, Level 1 Labs, Oct 2008 Variance (or Mean Squared Deviation) Example calculation of, &