Unit 1 Accuracy & Precision

 Data (Singular: datum or “a data point”): The information collected in an experiment. Can be numbers (quantitative) or qualities (qualitative).  Known: Substance that has specific (known) values. Used to calibrate experiments.  Unknown: Substance to be tested in an experiment.

 True Value: The “real” value of some property – this is often impossible to really know.  Accepted Value: The closest approximation to a True Value; agreed upon by most experts.

 Trial: A single run of an experiment.  Sample Size (n): The number of times an experiment is performed (# trials).  Should be at least 3 to ensure valid results. The larger n, the more confident we can be in the data.

 Mean (x): The average of all the trials. When reporting results, this is usually the final answer that is published.  This is also called the Experimental value.  Median: The central value in a sample. If there is an even number of trials, it is the average of the two central values.

 Maximum: Highest data point.  Minimum: Lowest data point.  Range (for data): A data set bordered by the Minimum and Maximum values.  Range (for a result): The reported result (average) with a certain amount of error  (± some number). e.g. 7.1±0.2

 Accuracy: A measure of how close a result is to the true or accepted value.  Measured by percent error.  One data point can be accurate, but it tells you nothing of the likelihood that the next value will be accurate.  When you have a group of results, the accuracy is based off of the mean (average) of your results.

 Precision: A measure of how close together data points are to each other.  It is measured by the standard deviation.  You must have > 1 data point in order to have precision. You must have a group or population of results in order to be precise.  The greater the precision, the greater the likelihood that your next value will be close to the previous one.  It is also called reproducibility or repeatability.

C.A.B.D.

 Percent Error: This is a measure of accuracy.  A percent error of <5% is usually considered accurate.  Its formula is: |True Value – Experimental | * 100 True Value -or- |True – x| * 100 True

 The Standard Deviation (σ): The standard deviation can be considered a range of values where the true answer lies.  It is a measure of precision. The smaller  relative to x, the greater the precision.  e.g. if your average result is 4.1 g and  σ is ±0.5 g, your true answer is 4.1 ±0.5 g.  This is 3.6 g to 4.6 g.

 You will not be responsible for calculating the Standard Deviation (yet), but its formula is:   = sqrt(  (x – x) 2 / n)

 Relative Deviation: This is a measure of relative precision.  The lower the relative deviation, the more precise.  An experiment can be considered precise if Rel Dev < 10%.  Its formula is Rel Dev =  / x *100

 Anomaly: A result that cannot be explained by current scientific understanding.  Often times, anomalies are simply the result of random errors.  Outlier: An anomalous result that lies outside of the specified range of acceptable values.  It may be discarded under certain circumstances.

 Interpolation : Using a set of data to infer an unknown value between the measured quantities. “Between the points.”  Extrapolation: using a set of data to infer an unknown value by extending the trend of the measured quantities. “Outside the points.”

What is the value when X = 2.5? Y = 12.5

What is the value when X = 0.5? Y = 2.5