Use these basic statistics to describe a set of measurements before you graph them. Each one tells you something different about your data.
You can calculate all of these in Excel, SPSS, or other statistical software.
Mean (average)
The mean is the average value of a set of observations. To calculate it, add all the figures and divide by the number of observations.
The mean is a form of continuous data. Graph it on a run chart over time.
The formula for calculating the mean is:
Total of all the observations ÷ Number of observations
Example
If you observed the following 12 numbers:
Mean = (19, 13, 18, 21, 44 ,17, 12, 31, 37, 8, 12, 27) ÷ 12 = 21.58 or rounded to 22.
Median
The median is the middle value when your observations are sorted from lowest to highest. Half the values fall below it and half fall above.
Use the median when:
- the data set is large
- the data is skewed or has outliers
- a normal distribution cannot be assumed (non-parametric data).
If you have an even number of observations, average the two middle figures.
Examples
Uneven number of observations: 8, 12, 12, 13, 17, 18, 19, 21, 27, 31, 37 = The median is 18.
Even number of observations: 8, 12, 12, 13, 17, 18, 19 21, 27, 31, 37, 44 = The median is 18.5.
Mode
The mode is the value that appears most often in a set of observations. It shows where the data tends to cluster.
Example
8, 12, 12, 13, 17, 18, 19, 21, 27, 31, 37, 44. The mode is 12.
Range
The range measures how spread out the data is. To calculate it, subtract the smallest value from the largest.
Range = largest observation minus smallest observation.
Example
8 12, 12, 13, 17, 18, 19, 21, 27, 31, 37, 44. The range is 44 minus 8, which is 36.
Standard deviation
The standard deviation measures how far each value tends to be from the mean. If the standard deviation is small, then most of the numbers are close to the mean. If the standard deviation is large, then the numbers are more spread out.
The standard deviation is found by taking the square root of the variance. To calculate the variance, take the mean and subtract it from each value in the data, then square each difference, and take the average of those squared differences. Then take the square root of this variation to calculate the standard deviation.
Use Excel or a statistical program for a precise figure.
If you are using population data, talk to a statistician to determine which calculation is better for you.