[Analysis of Data]

Standard Deviation

The standard deviation measures the average amount the data deviates from the average or mean of the data set.


S = Standard Deviation

= Sum of

= each data point in a data set

mean = the average of the data points

N = the number of data points.

The data table below represents turbidity (how dirty the water is) data which is being analyzed for standard deviation. In this case, X represents the mean.

Dividing 99.88 by ( 7-1) , we get a value of 16.65. We then take the square root of 16.08 which gives us a standard deviation of 4.08. We retain the .08 as the original turbidity data shown in the table above was accurate to 2 decimal places (as in 4.75, 3.45, etc).

Reporting data results with standard deviation:

The mean turbidity data may be reported as 8.09 +/- 4.08.

The lower the standard deviation, the greater the precision. In this case, the precision is not very good, as there is about a 50% variance in the data sets (4.08 is about 50% of 8.09)!

What Data do You Use to Calculate Standard Deviation?

To calculate S.D., look at your final graph of averaged data. What is your DV & IV on the graph? If it is reaction rate, then you must calculate the reaction rate for each of the trials at each concentration as in the table seen below. If you are calculating change in mass (DV) vs. concentration or drink, you would calculate the change for each of the trials of each concentration or drink. If it is change in volume, or change in length,you would do the same thing. If it is the percent change in mass/volume/ or length, you would do the same thing!

Notice that the standard deviation is calculated using the separate trial reaction rates plus the average reaction rate for each concentration in the example above! You can set it up like this for each of your individual labs using Microsoft Excel. Obviously, the labels, units and title will vary with each experiment!

[How to Use Standard Deviation to Compare Data Sets]

[Reporting Mean Data Using Standard Deviation Calculations]

[Calculating the Standard Deviation using Excel]

[Using Microsoft Excel to add standard deviation error bars to your graph.]

Courtesy of the Student Watershed Research Project.