Using Standard Deviationin AP Biology

Why would we use the standard deviation to analyze our lab result?

• In statistics and probability theory,standard deviation (represented bythe symbol σ ) shows how muchvariation or " dispersion " exists fromthe average (mean, or expected value)

• A low standard deviation (less than 2) indicatesthat the data points tend to be very close to the mean, whereas high standard deviation (greater than 2) indicates that the data points are spread out over alarge range of values.

What is the formula for standard deviation?

Note: since our data is a sample, not a population, we will use n-1 and not just n for our denominator.

What are the basic steps?• Step 1-Find the mean of the data (in other

words, take an average of all your data points)• Step 2-Subtract the mean from each data point• Step 3- Square of the values you got in step 2• Step 4-Subtract 1 from the number of data

points you used in step 1.• Step 5- Divide your answer in step 3 by your

answer in step 4.• Step 6 -Find the square root of the answer you

got in step 5.

Fun with standard deviation!

• Click on this website to access mathisfun.com

Use the standard deviation calculator on this website to try your hand at standard deviation problems!!

Youtube videos which help explain how to do standard deviation:

Watch this video to give you the basic steps in calculating standard deviation:http://www.youtube.com/watch?v=klP8ElkVxJk

This video gives two ways to calculate standard deviation (the computational formula is a little less work)http://www.youtube.com/watch?v=_x-XWDEIhfE

Watch this one to help you do standard deviation on a calculator:http://www.youtube.com/watch?v=DMOXzwC2vzg

Watch this one on using microsoft excel to calculate mean, variance and standard deviation:http://www.youtube.com/watch?v=efdRmGqCYBk

How to use your calculator to compute standard deviation

• Clear all data on your calculator.• Click on 2nd and then Stat button (above DATA)• You will see 1-var. This will help you get the standard deviation of a sample.• Hit enter• Hit Data• When you see X1 submit your first data point. Hit enter.• Then hit down arrow.• You will see FRQ- Enter how many times the same data point shows up in your results.• Hit enter. • Hit the down arrow. You will see X22. . Submit your next data point. Hit enter. Hit down arrow.• When frequency shows up, enter the number of times that data point shows up in your

results. Hit enter. Hit down arrow.• After all data points and their frequency are entered, hit stat/var button on your calculator.• Use the right arrow to display mean and sample standard deviation.