1. Cell Diameters and Normal Distribution

2. Frequency Distributions a frequency distribution is an arrangement of the values that one or more variables take in a sample. Each entry in the table contains the frequency or count of the occurrences of values within a particular group or interval. The table summarizes the distribution of values in the sample.

3. Variability Most biological samples show variability. Given this fact, how can we determine whether the differences we observe are significant, or merely random fluctuations?

4. Tally Chart Height range Number of students Cumulative number less than 5.0 feet25 5.0–5.5 feet3560 5.5–6 feet2080 6.0–6.5 feet20100 What is the interval?

5. The Normal Distribution A frequency distribution that is symmetrical around the mean is called a normal distribution. The common name: “the bell curve”

6. Normal Distribution A further requirement of a normal distribution is that the variable should be continuous, i.e. all values across the range are possible. Height range Number of students Cumulative number less than 5.0 feet25 5.0–5.5 feet3560 5.5–6 feet2080 6.0–6.5 feet20100

7. Standard Deviation Standard deviation is a measure of the range of variation from an average of a group of measurements.

8. AP Biology Exam has reference tables!

9. Standard Deviation For a normal distribution, 68% of all measurements fall within one standard deviation of the average, or mean. 95% of all measurements fall within two standard deviations of the mean.

10. Standard Deviation Graphically Think of SD as a measure of the spread around the mean…

11. Use the following procedure to investigate the distribution of cell diameters in figure 2. Measure the diameters of all the cells of one type in figure (a tally sheet) Enter your data as a tally chart on excel in a single column.

12. Making a Graph Use Excel to construct a histogram to display the percentage of cells in each category. If your curve is bell-shaped, it is probably a normal distribution. Print out a copy of your graph and attach to your data. Write a short comment on your graph about the shape of the curve.

13. Annotating Your Graph Make a line graph of your distribution, and plot the mean as a line, a single standard deviation, and two standard deviations from the mean on the graph. Shade in the areas bounded by these values.

14. Using Excel Using the formula functions of excel, calculate the mean and the standard deviation of your sample. Divide the cells up into a series of size categories. Using excel, determine the frequency for each size category as a fraction of 1.0.

15. Explain the significance of values that are 1 and 2 standard deviations from the mean of a normal distribution.

16. Sources of Error Consider any sources of error you might have encountered (think of several)…