AP Biology Unit 0: Graphing and Stats

Bar Graphs

This uses rectangular bars to visually compare quantities between different, discrete categories (are characteristics that can be sorted into a few distinct, non-overlapping groups, there are no in-between or intermediate forms) that are not continuous over time. (meaning these traits do not gradually blend or change smoothly, but rather represent distinct, separate states at any given moment)

Such as the number of species in various habitats or the mean population size of a fish species in two different lakes.

The height or length of each bar corresponds to the measured value for its respective category, allowing for quick and easy comparison of these separate groups.

Line graph

A _______ ______ is a type of graph that shows how a variable changes over time or in response to another variable. it uses points connected by lines.

_____ ______ are used to show trends, such as changes in temperatures, enzyme activity over time, population growth, or reaction rates in experiments.

Histogram

It is a type of bar graph that is a visual representation of the distribution of continuous data (is any data that can be measured on a smooth un-broken scale, including fractions and decimals. This type of data shows a wide range of values between two extreme with no distinct categories), such as time, weight, or temperatures. Using bars to show the frequency of data points within defined intervals or “bins” (is a range of values)

Unlike a bar chart, a histogram has no gaps between its bars, which represent adjacent ranges of values.

__________ are used to show how often certain values occur, such as the frequency of trait sizes, heights of plants, or test scores in a population. They help visualize variation and patterns in data.

Scatter Plot positive correlation

A ______ _____ _______ _______ shows the relationship between two variables using dots. A _____ _______ means that as one variable increases, the other also increases.

This is used to show relationship between two biology variables, like the increases in enzyme activity as temperature rises up, or height vs biomass in plants. This helps identify trends or correlations from data of two different variables.

Scatter plot negative correlation

A _____ _____ ______ _____ uses dots to show the relationship between two variables. A ______ ________ means that as one variable increases, the other decreases.

This is used to show inverse relationships, like the decreases in enzyme activity as pH moves away from the optimum, or increases pollution leading to lower biodiversity, This helps identify negative trends in data.

Scatter plot No correlation

A _______ _____ with __ _______ uses dots to show data for two variables. ____ ________ means there is not clear pattern—one variable doesn't affect the other.

It is used to show that two variables are unrelated, like plant heights vs. color of flower, or enzyme activity vs moon phase. This helps show lack of connection in data.

Pie charts

It is a circular graph divided into slices, where each slice represents a part of a whole and its size is proportional to its percentage of the total.

You would use it to show, for example, the percentage composition of gases in the atmosphere or the distribution of different traits within a population at a single point in time.

It is used to show how different categories contribute to a total, like the percentage of different blood types in a population, types of organisms in an ecosystem, or sources of carbon emissions. It helps visualize proportions clearly.

Dual Y

Is a graph that has two vertical axes (Y-axes) to show two different variables on the same graph, each with its own scale, each responding to the same independence variable over time.

It is used to compare two related sets of data, like temperature and enzyme activity, or light intensity and photosynthesis rate. It helps show how two variables change together, even if they used different united or scales.

Logarithmic

This uses a scale where each unit increases by a power of 10, helping show large ranges of data more clearly.

It is used when data spans several order of magnitude, like bacterial growth, pH levels, or population size over time. This helps visualize rapid changes or exponential trends in biological.

A box and Whisker Plot

This graph shows the spread and distribution of a data set using a box and lines (whiskers). It highlights the median, quartiles, and outliers.

It is used to compare variation within or between groups—like plant heights under different light condition or enzyme activity at different pH levels. This helps show the range, spread and consistency of biological data.

It is useful because it shows the spread of data, whether the data is skewed, If there are any outliers, How two or more groups compare in terms of variation.

How to plot a Box and Whisker Plot

1. Minimum— the smallest value (excluding outliers)

2. First Quartile (Q1) — 25% of the data falls below this point

3. Median (Q2) — the Middle value (50% of data falls below it)

4. Third Quartile (Q3) — 75% of the data falls below this point.

5. Maximum — the largest value (excluding outliers)

The box shows the range from Q1 to Q3 (clawed the Interquartile range or iQR)

A line inside the box marks the median

The whisker extend from the box to the minimum and maximum values

Outlier are sometimes shown as individual dots beyond the Whiskers

Graph Construction

The process of making a graph that shows the relationship between variables in an experiment for AP bio has requirements in order to get these points, which include:

1. Graphs (called figures) should have a concise, explanatory title. They should be numbered consecutively in your report.

2. Plot the points accurately. So different responses (different dependent variables) Can be distinguished using different symbols, lines, or bar colors.

3. Label both axes (Provide Scientific Units of measurement if necessary)

4. The responding variable (dependent variable) is plotted on the vertical y axis

5. The Manipulate variable (independent variable) is on the horizontal (x) axis.

6. Make sure to put an Axis break which is a squiggle in the axis that skips empty space where no data exists.

7. Make sure to put a floating axis which is when the graph doesn’t start at zero, so the data is shown away from the edge.

8. The Spread of the data around the plotted mean value can be shown on the graph. The standard deviation values are plotted as error bars.

9. A key identifies symbols. This information sometimes appears in the title.

10. Each axis should have an appropriate scale. Decide on the scale by finding the maximum and minim values for each variable.

Error Bars — Standard Deviation.

These are lines on a graph that shows how spread out or uncertain the data are. They tell you whether your measurements are consistent or variable (spread out).

There are three common types of these (Ap bio mostly uses standard deviation)

1. Standard Deviation (SD)

   1. Measures spread of the data points around the mean.

   2. Bigger SD — more spread out data

   3. Error Bars are drawn as: Mean±SD (You use the standard deviation as the length of the error bar, to show the data’s spread or variation)

      1. plot the mean of your data, then draw a cap-tipped line extending above and below that mean by the value of your calculated Standard deviation.

2. How to calculate the Standard deviation:

   1. Find the Mean: Add up all the values in the data set and divided the sum by the total number of values in the set to get the mean.

   2. Calculate the Deviations: For each data point, subtract the mean from the value of that data point (data point - mean)

   3. Square each of the difference values you found in the previous set. This makes all the of values positive.

   4. Add up all the squared Deviations together

   5. Calculate the variance—for a population: Divided the sum of the squared deviations by the total number of data points (N)

   6. Calculate the Variance—for a sample: Divided the sum of the squared deviations by the number of data points minus one (N-1) (Is Bessel’s Correction)

   7. Take the square root: Take the square root of the result form the previous step to find the standard deviation.

Error bars — Stander Error of the Mean

These are lines on a graph that shows how spread out or uncertain the data are. They tell you whether your measurements are consistent or variable (spread out).

This is the second type of one:

1. _______ _____ of the mean

   1. This measures how precisely you know the mean

   2. Formula: SE= SD / square root of the total number of data points (not sum)

      1. n = the total number of data points

      2. The Standard Error Is smaller when you have more data points.

   3. To create this you add and subtract the standard error value to and from the men for each data points or category.

Error bars — Confidence interval

These are lines on a graph that shows how spread out or uncertain the data are. They tell you whether your measurements are consistent or variable (spread out).

This is the third type:

1. Confidence interval (Cl, often 95%)

   1. This is a range where the true mean probably falls

   2. A 95% CL means: if we repeated the experiment many times, 95% of the intervals we calculate would include the real mean.

   3. It does not mean we are 95% sure this single interval has the true mean— it's about long-term reliability.

2. How to Calculate an Confidence interval:

   1. CL = xˉ±(t×SE)

      1. xˉ = is the sample mean

      2. SE is the standard error of the mean

      3. t = value from the t-distribution table (depends on sample size and desired confidence)

         1. For large samples, t = 2 (AP Bio usually just assumes 95% CL = meaning ± (2 x SE)

3. How to interpret for example: We’re 95% Confident the true mean enzyme activity lies between 10 and 14 units

4. If another groups 95% CL doesn't overlap with this one, it suggests a meaningful differences and we can move on to conclude something.

How to read Error Bars

1. If their is a short error bar that means the Data is very consistent

2. If there is a long error bar that means the data is more variable

3. If error bars overlap a lot that means the difference between groups many not be meaningful—its inconclusive if trying to make a claim when analyzing the data.

4. If they don’t overlap much that means the groups may truly different and claims can be meaningful.

When you go to the doctor why did the doctor ask questions and what did they measure.

Doctor ask questions and take measures because they are collecting variables to analyze patterns, much like scientists graph data.

By eliminating confounding variables (is an uncontrolled factor that influences both the independent and dependent variables in an experiment, creating a false or misleading correlation, it confuses the true relationship you are trying to measure) and narrowing possible links, they increases the statistical significant of their evidence, allowing them to make a more accurate and effective diagnosis.

Science

Different fields of study that attempt to comprehend the nature of the universe.

Hypothesis

A suggested explanation for an event, which can be tested.

For example, _________: if plants are given increases amounts of light, then their rate of photosynthesis (measured by oxygen production), will increases, because light is a key independent variable that drives the process of photosynthesis.

Most commonly includes the if…(independent variable)…then…(dependent variable)…Because…. format.

Theory

A well tested and confirmed explanation for observations or phenomena.

Deductive reasoning

The use of logical thinking to predict results by applying scientific principles or practices.

In AP Bio, deductive reasoning usually starts from a broad biology principle (theory, law, or known mechanism) and applies it to a particular case or prediction.

Scientific method

A step-by-step process that consists of:

1. Making observations

2. Defining a problem

3. Posing hypotheses

4. testing these hypotheses by designing and conducting investigations (like experiments)

5. Drawing conclusion from data and results.

Variable

Any part of the experiment that can vary or change during the experiment.

Control group

Contains every feature of the experimental group except it is not given the manipulation that is hypothesized about

For example, if you are testing how fertilizer (independent variable) affects plant growth (dependent variable), the control group would be plants given no fertilizer, but with the same conditions with the experiment group, so you can compare their growth to the experimental groups.

Independent variable

The experiment changes/manipulates this during the design of the experiment.

It is the factor that the experimenter changes on purpose to tests its effect on the outcome (dependent variable)

For example, in testing light on photosynthesis, light intensity is the independent variable.

Dependent Variable

This is what changes in response to the independent variable

Is the factor that is measure in an experiment; it changes in response to the independent variable.

For example in testing light on photosynthesis, the rate of oxygen production is the dependent variable.

Null hypothesis

It is a statement of no significant difference between the variables—they are not related.This can often be consider the status quo. And this is where any different is considered purely by chance. In Science individuals are trying to rejected the null hypothesis and find some type of correlation.

Is a prediction that the independent variable will have no effect on the dependent variable;any difference in results is due to chance

Alternative hypothesis

It is a claim about the population that is contradictory to H0 (the Null hypothesis) and what we conclude when we cannot accept the H0 (the Null hypothesis). This is usually what the researcher is trying to prove. The _______ _____ is a contender and must win with significant evidence to overthrow the status quo.

Or it is a predicting that the independent variable does affect the dependent variable and explains the observed results, for example, increasing light intensity will increase the rate of photosynthesis.

Scientific theories are subject to revision as new information is collected. Why do scientists say they have evidence that supports a hypothesis/theory and rarely say they have proved something

Scientists say they have evidence that supports a hypothesis or theory instead of saying they’ve “proved” it because sciences is always open to new data and there are too many variables to completely rule out other explanations.

Just like medical ads can’t claim a drug “solves” a condition—since different variables affect patients—scientific conclusions are supports, not absolutely proven.

For example Scientists may say, “Data supports that smoking increases lung cancer risk,” but they won’t say it’s “proved,” because other variables like genetics and environment also play a role—-similar to how medicine ads can’t claim a pill completely cures everyone.

If an experiment is truly a controlled experiment, and if the results of the experimental group different from the control group, explain why the difference is likely due to the hypothesized manipulating rather than some outside factor.

In a controlled experiment, all variables except the independent variables are kept constant. So, if the experimental group different from the control group, the difference is most likely due to the manipulated variable, not outside factors.

Experiments are complex, and often involve considering more than just the independent and dependent variable. What would a “controlled variable” be in an experiment.

A controlled variable is any factor kept constant in an experiment so it doesn’t affect the results.

For example, when testing light on photosynthesis, keeping the amount of water and type of plat the same are controlled variables.

What would it take to convince someone that variations in data were not purely by chance

To convince someone variations in data aren’t just by chance, scientists use statistical test to show the results are statistically significant—meaning the differences are likely caused by the independent variable, not random error.

For example an experiment that test if fertilizer increases plant growth the control group is plants with no fertilizer and the experimental group is the plants with fertilizer. If the fertilized plants grow significantly taller than the control group, and statistical tests show the difference isn't due to chance, we can conclude the fertilizer (independent variable) caused the change.

Conclusions among null and alternative hypothesis.

Since (Evidence) we Do Not HAVE significant Evidence against the Null Hypothesis. We FAIL TO REJECT THE NULL HYPOTHESIS as our results are LIKELY “purely by chance.”

OR

Since (Evidence) we HAVE significant evidence against the Null Hypothesis. We REJECT THE NULL HYPOTHESIS as our results are UNLIKELY “purely by chance”

Essential knowledge for setting up an conclusion from an experiment.

1. Determine Scientific questions and methods

2. Identify or pose a TESTABLE question based on an observation, DATA, or a MODEL

3. State the NULL and ALTERNATIVE hypotheses, or PREDICT the results of an experiment.

4. Identify experimental procedures that are aligned to the question, including:

   1. Identifying Dependent and Independent variables

   2. Identifying appropriate controls

   3. Justifying appropriate controls

5. Make Observations, or collect DATA from representations of laboratory setup or results

6. Propose a new/next investigation based on

   1. An evaluation of the experimental design/methods or evidence from an experiment

7. APPLICATION: (can you determine scientific questions and methods, and explain biological concepts, process, and models presented in written format)

Descriptive Statistic

Numbers that summarize and describe data, like averages, ranges, and standard deviations, without making conclusion about a large population.

It is used to describe where your information is located among the data set.These are calculated from measured data points and are not individual data points themselves.

For example if you measure plant heights (data points: 10cm, 12cm, 14cm) that average height (12cm) or standard deviation is a ______ ______ summarizing those measurements.

We used _____ _____ to summarize our collected data and provide insight int our experimental results.

If someone is considered “average height” — What does that mean? Is that an actual measured number.

Being “average height” means a person’s height is close to the mean of a population, not a single exact number. It’s a statistical summary using a descriptive statistics (mean), not an individual measurement.

It is used to describe where you are within the data.

How would your height be different if it was considered the mode or median.

If your height is the mode, it’s the most common height in the group. If it’s the median, it’s the middle value when all heights are arranged in order. Both are descriptive statistics, not exact measurements of every individual.

What is the difference between your actual height and the answers above.

Your actual height is a measured number for your personally, while the mean, media, or mode are summary statistic/descriptive statistics that describe a group or where you are within the data points, not your exact value.

Mean

Is a descriptive statistics that is the average value of a dataset

The mean is caused by summing all the values in a dataset and then dividing that sum by the total number of data points in the set.

Mode

Is a descriptive statistics that tell the value that occur most frequently in a data set.

Median

It is a descriptive statistics that tells the middle value that separates the greater and lesser halves of a data set.

It is calculated by arranging data in numerical order, select middle most value.

Range

It is a descriptive statistics in where the value is obtained by subtracting the smallest observation (sample minimum) from the greatest (sample maximum)

(Sample max

Normal distribution

This represents data that cluster symmetrically around a central average value (mean), forming a characteristic “bell curve” shape.

It’s a common model in the natural and social sciences for phenomena like human height or measurement errors, where most values are near the average, and values further away occur with decreasing frequency. Key characteristics include symmetry, a single peak at the mean, and values defined by the mean and standard deviation.

A _____ _______ is fully described by its mean (the center of the bell) and standard deviation (which measures the spread or width of the curve)

Standard deviation

Is the measure of how spread out or variable a data set is from its average (mean).

A small standard deviation means data points are clustered closely around the mean, indicating consistent results, while a large standard deviation suggest data is widely dispersed, signifying greater variability.

It provides a precise number for how much data points vary from the average, which is essential for analyzing biological phenomena.

If you were to randomly pick a data points, that point would (on average) be 1 S.D away from the mean.

It is often represented with +/- as your value could be either above or below average.

Standard deviation is used in the context of a normal distribution (bell curve), where:

1. 68%: of data falls within one standard deviation of the mean

2. 95%: of data falls within two standard deviations

3. 99%: of data falls within three standard deviations

When comparing different data sets or experiments, standard deviation helps determine which set is more consistent or variable.

A large standard deviation.

A large _____ ______ indicates that the data points in a sample are widely spread out, meaning that there is a lot of variation or dispersion from the mean (average)

For example, you are comparing the average photosynthetic rate of two types of plants, Plant A and Plant B, exposed to the same light intensity. Plant A has a large standard deviation in its photosynthetic rates (e.g., 1.0) while Plant B has a small standard deviation (e.g., 0.2)

This implies Plant A’s data shows that its photosynthetic rates are very inconsistent, with some individuals having very high rates and others very low ones, even though their average might be the same as Plant B’s.

large standard deviation suggests significant biological variation within the group being studied. This could be due to genetic differences, environmental influences, or other external factors affecting the trait.

This means the data points are less reliable in representing a single, uniform values.

A widespread data may indicate that the trait being measures is influenced by multiple factors, or that the condition were not uniform for all subjects in the sample.

A small standard deviation

A small _____ _______ indicates that your data points are clusters tightly around the mean, meaning there’s low variability and high consistency in your results.

For example, if you measure the leaf lengths of many plants in the same species, s small standard deviation would show that most leaves are very close in length to the average leaf length.

This implies that the experimental condition were very consistent, the organism’s traits are similar, or the measurements are very precise.

It further implies that the biological samples or organism being studies are very similar, or the experimental conditions were tightly controlled.

Moreover that the process you used to collected the data was consistent.

And your measurements are likely accurate because repeated measurements show similar results, supporting the validity of your findings.

Standard Error of the Mean

This is a descriptive statistics that helps establish confidence intervals about the predicted distance from the sample mean of data from the true population mean.

Examples _____ _______ __ ___ _____ = +/-2.4 Mean = 14. Confidence interval (11.6, 16.4) = the true mean is likely to fall between this, and the sample mean would vary between this range if you repeated the experiment many times.

It shows how much the sample mean would vary if you repeated the experiment many times. It’s like a special kind of standard deviation that measures the accuracy of the mean, not individual data points.

To calculate the _____ ____ ___ ___ _____ you do SEM = SD/ square root of sample number.

For example: if you measure the height of 5 plants and get an average of 12cm, the _______ ______ ___ ____ ___ (SEM) shows how much that average (12cm) would likely change if you measured 5 new plants again.

What does a Small standard error of the mean indicate

A small standard error of the mean means the sample mean is close to the true population mean, so your data gives a reliable estimate of the real average

What does a large Standard error of the mean indicate

A large standard error of the mean means the sample mean is less reliable and may be far from the true population mean, showing more variation in the data.

How does Sample Size (N) affect the accuracy of statistics

A Small sample size increases the chance of outliers messing up the mean and makes error bars larger, so the results look less reliable.

But with a bigger sample size, the effect of outliers is reduced, error bars get smaller, and the mean becomes a more accurate estimate of the true population value.

Are any of these descriptor/ statistics influenced by outliers in a data set

yest—the mean and range are strongly influenced by outliers, since on extreme value can raise or lower them a lot.

The median and mode are less affected, making them more reliable if the data set has outliers. In AP bio this matters because outliers can distort results and affect how we interpret variability in experiments.

Explain the term inferential statistics and how does your definition relate to confidence intervals and error bars.

Inferential statistics use data from a sample to make conclusions about a larger population.

In Ap biology, this related to confidence intervals and error bars because both show how reliable the sample data is—narrow intervals or small error bars mean we can be more confident that the sample reflected the true population.