Graphing and Data Analysis
(Statistics)
MUST DO’s in Graphing
1.
Title: The effect of IV on DV
2.
IV on the X axis
3.
DV on the Y axis
 Indicate on each axis what is being measured
and in what units
 Time (Min)
 Distance (meters)
 Water loss (mL/m2
Determine range & scale
4.
1.
Scale~ best fits the range
2.
Use MOST of the area
3.
The graph should clarify whether the data
start at the origin (0,0) or not.
Key/Legend (for more
5.
one set of data)
◦
If you are plotting more that one condition or data
set, use different lines or symbols for each data set
such as circles, squares, triangles
“DRY MIX” –
means what?
Get the CAKE POINTS!

Earn essay points just for
stating the obvious.
◦ “The independent variable is…”
◦ “The dependent variable is…
measured in…”
◦ “___ is the control (group)
because…”
◦ “Control variables should
include…”
◦ “The hypothesis is that
if…then…”
◦ Discussing analysis of data
◦ Drawing conclusions about data
MUST DO: Plotting Points

Determine a KEY
Connect Your Data Points
• Start with first data point- not zero
• Connect only the data points- do not
extend before or beyond the data
points
• Extrapolate with dotted lines if a
prediction needs to be made
Graphing & Interpreting Results
Line Graphs
◦ To interpret rate (slope)
◦ Quantitative X and Y axis
(which means what?)
 What if slope is straight,
horizontal line?
The Effect of Length of Worms on
Number of Worms Found
Number of Worms

Worm Length (cm)
Graph Interpretation

What can
you gather
from these
graphs?
The Effect of Time on Population
Reaction Rate (mg/sec)
The Effect of pH on Enzyme Activity
pH
Graphing & Interpreting Results

Scatter Plot
◦ Display entire sets of
data
◦ Bivariate - Use when
comparing 2 variables
(so not just 2
independent variable
being measured on yaxis.You have 2
separate variables you
want to measure)
 DRY MIX doesn’t work
with these – why?
◦ Shows relationships or
correlations between
variables
Number of Wal-Marts vs Number of
Starbucks per Million People
What’s the correlation?
Scatter Plots
Suppose that we want to graph the heights and weights of a group
of people.
Since both height and weight are variables, we use the phrase
bivariate data, meaning that there are two variables.
Bivariate data are best displayed on a scatter plot or scattergram.
 Each data point represents both an x value and a y value. In our
example, the coordinates of a point are (weight, height).
 Do NOT connect the points. This is because each point represents a
particular fact. In our example, the “fact” is one person.
 After you plot all the points, look at them to see if there is a trend, a
pattern.
 If the points form a pattern that tends to rise, we say that there is a
positive correlation.
 If the points form a pattern that tends to fall, we say that there is a
negative correlation.
 If the points do not show any organized pattern, there is no
correlation.
No correlation
Let’s do it. Graph these data.
Answer
Graphing & Interpreting Results
Bar Graphs
◦ Qualitative or categorical data
 Which means what is going to be on the x-axis?
The Effect of Type of Animal on Heart Rate
Heart Rate (beats per minute)

Domesticated Animals
Let’s try one.
Country
Algeria
Brazil
Hungary
Guatemala
HIV Prevalence in ages 1549
1990
0.06
0.45
0.10
0.10
2009
0.10
0.45
0.06
0.60
Answer
HIV Prevelance in Ages 15-49
0.7
%
0.6
H
I
V 0.5
i
n 0.4
1990
a
g
0.3
e
s
2009
1 0.2
5
4 0.1
9
0
Algeria
Brazel
Hungary
Guatemala
Analysis of data: Mean, SD (Standard
Deviation) and SE (Standard Error
of the Mean)
If the data has a normal distribution we
can find the mean, SD and SE
 Mean – summarizes the entire sample

◦ If a large enough sample size is used it may
estimate the actual population’s mean.
◦ Even so, the mean can often be misleading
because it suggests to show a representation
of all of the data. If the data range is very wide
then the average may not truly tell the whole
story.
SD – Standard Deviation
Measures the spread (variance) in the sample
 Large SD indicated that the data have a lot of
variability (very big range)
 Small SD indicates that the data are clustered close
to the sample mean (very small range)
 SD applies to the data set at hand

You will not be asked to calculate standard deviation or standard error of the
mean (SEM) because it is too time consuming for the time allotted on the AP
exam. Even so, standard deviation and SEM CAN BE USED on the exam with
questions asking you to interpret the meaning of these values or to apply them
to a data set/graph.
You may see an average that say 8.6 +/- 2.3. This means that the mean was
8.6 with a standard deviation of 2.3. So, using the Standard Deviation we have
a "standard" way of knowing what is normal, and what is extra large or extra
small.

Equation
x = mean
 n = sample size
 xi = individual value


** Note:You may have used a different equation in statistics. I can
explain the difference if you need me to.
SE- Standard Error

Allows us make an inference about how well the
sample mean matches up to the true population
mean.


s = the sample SD
n = the sample size
The larger the sample of the population, the smaller
the SE to the actual population.
 Difference between SD and SD:

◦ Standard Deviation applies to the data set at hand
◦ Standard Error of the Mean applies to the general
population
Chi-squared: Rejecting or failing to
reject (accepting) a hypothesis in an
experiment

The null hypothesis states “There is no
difference between the expected and the
observed”

A X2 analysis will help determine if the
difference between what you observed
and what you expected is statistically
significant or not.
Equation: Scary looking but not so
bad

•So what does it mean???
O = observed data
E = expected data
Σ = sum of…….
The equation is used for each group in the
experiment, and the values are added together




This will give you the chi-squared value. Now what?
First,You must now find your degrees of freedom.
Degrees of freedom is the number of independent random
variables involved.
Degrees of freedom is simply the all of your possible choices minus
1.
◦ Marker Example


There is a table for chi-squared on your equation sheet. We always use p
(probability) of 0.05 which means there’s a 95% chance that any difference
between the expected and observed value is due to chance.
The intersecting point of our degrees of freedom in the 0.05 column gives us our
critical value.
◦ If chi-squared is less than our critical value then we “fail to reject” our null hypothesis.
In other words, there is no statistical difference in the expected results and what we
actually saw.
◦ If chi-squared is more than our critical value then we reject our null hypothesis
indicating there is a statistical difference in the expected and observed results.
◦ M&M chi-squared.
To sum it up…..


Standard error of the mean is an estimate of how close your
sample mean is to the actual population’s mean
Standard deviation is the degree to which individuals within the
sample differ from the sample mean

You will not have to calculate these values.

You should understand what it tells you and where it comes from.
SEM bars. If
there is overlap,
then there is no
statistical
difference
between the
groups
Graph Interpretation

What are the lines on each bar, and
what do they mean?
(H1N1 = Swine Flu)

What can you gather from this
graph? Is anything misleading?
Graphing & Interpreting Results
Histograms
◦ Plot density of data
(comparing different
amounts of data at
different points)
◦ Consecutive intervals or
categories
◦ Different than bar graph
because x-axis is a
CONTINUAL RANGE
◦ Different than a line
graph: Line graph = Line
graphs connect data
points that are somehow
related. Histograms
display distibutions of data
(how much in certain
ranges).
Scores on Final Exams
Number of Students

Exam Scores (maximum 100)
Graph Interpretation

What can you gather
from this graph?
Summary: When do I use each type of graph?
Bar Graph/Histogram
•
•
•
Comparing SET VALUES OF CATEGORICAL DATA (data that is finished
and will not change)
• Examples of categorical data
 size of a population by age range
 Number of deaths by causes of death
 Size of different populations in an ecosystem
May be used to calculate the means with error bars of normal data
Use Histogram when the categorical data is changing over a CONTINUAL
RANGE
Line Graph
•
Connect data points that are SOMEHOW RELATED and show a
CONTINUAL CHANGE OVER TIME.
Scatterplot
•
Bivariate - Use when COMPARING 2 VARIABLES
• So not just 2 independent variable being measured on y-axis. You
have 2 separate variables you want to measure
Age Pyramids for
different countries


What can you gather about the ages of
the citizens in these countries?
What can this tell you about the
country?
1. R
2. 0
3. 1,5
What is wrong with this graph?
Draw your answers here
Draw your answers here
ESSAY 2002
The activities of organisms change at regular time intervals. These changes are
called biological rhythms. The graph depicts the activity cycle over a 48-hour
period for a fictional group of mammals called pointy-eared bombats, found on an
isolated island in the temperate zone.
a. Describe the cycle of activity
for bombats. Discuss how
3 of the following factors
might affect the physiology
and/or behavior of bombats
to result in this activity pattern.
 temperature
 food availability
 presence of predators
 social behavior
b. Propose a hypothesis regarding the effect of light on the cycle of activity in
bombats. Describe a controlled experiment that could be performed to test
this hypothesis, and the results you would expect.
2005
2007