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Transcript
Cell Diameters and Normal Distribution
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.
Variability
• Most biological samples show variability.
• Given this fact, how can we determine
whether the differences we observe are
significant, or merely random fluctuations?
Tally Chart
Height range
less than 5.0 feet
5.0–5.5 feet
5.5–6 feet
6.0–6.5 feet
What is the interval?
Number of
students
25
35
20
20
Cumulative
number
25
60
80
100
The Normal Distribution
• A frequency distribution that is symmetrical
around the mean is called a normal
distribution.
• The common name: “the bell curve”
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
less than 5.0 feet
5.0–5.5 feet
5.5–6 feet
6.0–6.5 feet
Number of
students
25
35
20
20
Cumulative
number
25
60
80
100
Standard Deviation
• Standard deviation is a measure of the range of
variation from an average of a group of
measurements.
AP Biology Exam has reference tables!
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.
Standard Deviation Graphically
• Think of SD as a measure of the spread around
the mean…
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.
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.
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.
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.
Explain the significance of values that
are 1 and 2 standard deviations from
the mean of a normal distribution.
Sources of Error
• Consider any sources of error you might have
encountered (think of several)…