1. AP Biology: Standard Deviation
Carol Leibl
National Math and Science Initiative
Dallas, TX

2. Standard deviation
A statistical computation that is about how far members of the population deviate from the mean is the standard deviation. It is a characteristic of the population, so it doesn't depend on how many members you sample (except that if you only sample a few members, you won't get a good estimate of SD).

3. Two Different Normal Distributions
These two histograms have the same mean of five but they differ in their variation or range of values.
Histogram 1 has a range of 8 units and histogram 2 has a range of 4 units. There is more variation in histogram 1.
Both form a normal distribution.

4. Steps for Determining Standard Deviation
Determine the mean for the set of data.
Find the difference between each data point and the mean and then square the difference.
Sum all squared differences
Divide by the number of data point less one.
Finally take the square root of this number.

5. Your Turn Determine the Standard Deviation for this Sample
Have the students determine the standard deviation for this example.

6. Determine the s for either the black-eyed peas or pinto beans.
Your Turn
Have the students determine the standard deviation for this example.
Determine the s for either the black-eyed peas or pinto beans.

7. Two Different Standard Deviations
The standard deviations, s, for the two diagrams below are different. s=2.053 for histogram #1
s=1.046 for histogram #2
This makes sense because histogram #1 has more deviation from the mean or more variation in the data points.

8. Interesting Facts About Standard Deviations and Normal Distributions
The percentage of data points in a normal distribution that fall within plus or minus 1 standard deviation is 68.26%
and the percentage of individuals falling within plus or minus 2 standard deviations is 95% and 3 standard deviations is 99%. This is often called the % rule.

9. Interesting Facts About Standard Deviations and Normal Distributions
Both of the frequency distributions on the right form a normal distribution. The % rule applies to both distributions.

10. Two Different Standard Deviations
In histogram 1- 68% of all the data points fall between and % of all the data points fall between and
In histogram 2- 68% of all the data points fall between and % of all the data points fall between and 2.908

11. Averaging or Determining What is Normal
Shown are the histograms illustrating the frequency distribution of the mass of 300 black-eyed peas and 300 pinto beans.
Mean S
Black-Eyed Peas
0.21
0.042
Pinto Beans .37
0.37
0.074

12. Your Turn
A student was measuring the height of mung beans. The height of 200 plants was measured. The mean height of the mung beans was 4 cm and the standard deviation was .5 cm. What percentage of the plants had a height of 4 and 4.5 cm?
What percentage of the plants had a height between 3 and 4 cm?

13. Your Turn
A student is germinating lettuce seeds in a petri dish and after three days, 95% of them are between 1.1 cm and 1.7 cm long. Assuming that the data is normally distributed determine the mean and the standard deviation.

14. Your Turn
A student is measuring the mass of pill bugs and finds that 99.7% falls between .034 g and 0.18 g. Assuming that the data is normally distributed determine the mean and standard deviation.

15. Averaging or Determining What is Normal
It is possible to compare the means of the two populations using a simple bar graph. One bar representing the mean mass for each seed. The standard deviation or variation of the two populations can be represented by using vertical error bars.

16. Bar Graph with Illustrating the Means
Seed
Mean S
Black-eyed Peas
.21
.042
Pinto Beans
.37
.074

17. Bar Graph with Illustrating the Means and + 1 s
The represents the that variation that exist within 68% of the data points. It illustrates that the pinto beans has a greater variation in its sample population than the black-eyed peas.

18. AP Biology Content Specialist
Carol Leibl
AP Biology Content Specialist