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Step 7B: Using Statistics to Analyze Data

Statistics are established methods used by researchers of all kinds to analyze data. The methods for statistical analysis will help you interpret your measurements accurately and support your conclusions. Here are some common statistical methods you may use to analyze your data.

Mean, median, and mode.
The average of the data is also called the mean. The average is the value you expect to get when performing a specific trial of an experiment. It is calculated by adding all of the numbers in the data set, then dividing the sum by the number of trials.

The median is a measure that is used to identify the value for which one-half (50%) of the observations will lie above that value and one-half will lie below.

The mode is the value which occurs most frequently in the sample.

Probability. Probability is the likelihood of a given event's occurrence, which is expressed as a number between 1 and 0.

T-test. The t-test is the most commonly used method to evaluate the differences in means between two groups.

Variance. Variance is a measure of how much the data set varies from the mean.

Range. The range of a data set is the difference between the highest and lowest values in the set.

Standard deviation. The standard deviation is a measure of the spread of your data. The steps for calculating the standard deviation are:

  1. Compute the mean for the data set.
  2. Compute the deviation by subtracting the mean from each value.
  3. Square each individual deviation.
  4. Add up the squared deviations.
  5. Divide by one less than the sample size.
  6. Take the square root.

Experimental error. Experimental error is the difference between the measured value and the actual or known value of measurement. There are two types of experimental error, random and systematic

All experiments have random errors because no measurement can be made with complete precision.  The best way to identify and measure random error is to repeat the measurements and/or the entire experiment to get a range of measurements and identify the mean.

Systematic errors appear as a bias, or tendency, of your data to cluster together.  In this case, repeated measurements give you the pretty much the same result rather than a range. This kind of error can be caused by instruments that need to be re-calibrated.

To calculate experimental error, subtract the actual or known value of something from the experimental value (the measurement you made). Divide this number by the actual value.

(experimental value) – (actual value)
(actual value)