Math, Graphing, and Data Analysis

Independent variable

The variable that is changed on purpose; placed on the x-axis.

Dependent variable

The variable that is measured; placed on the y-axis.

Graph title format

Written as "Dependent variable vs. Independent variable."

Graph requirements

Includes title, labeled axes, units, proper scaling, plotted data, and trend line when needed.

When to use a line graph

Used to show changes over time or continuous data.

When to use a bar graph

Used to compare categories or groups.

Trend line

Showcases the general pattern or direction in data.

Identifying data points

Finding specific values directly from a graph or table.

Describing trends

Explaining patterns such as increasing, decreasing, or constant changes.

Describing relationships

Explaining how one variable affects another.

Mean

The average of data values; sum of values divided by number of values.

Percentage change

(new value − old value) ÷ old value × 100.

Rate of change

Change in a variable over time (Δy/Δt).

Ratio

Comparison of two numbers or quantities.

Water potential equation

Ψ = ΨP + ΨS (water potential = pressure potential + solute potential).

Solute potential equation

ΨS = −iCRT.

Ionization constant (i)

Number of particles a solute forms in water (e.g., NaCl = 2).

Gas constant (R)

R = 0.0831 L·bar/mol·K.

Temperature in Kelvin

Calculated using T(K) = °C + 273.

Gibbs free energy equation

ΔG = ΔH − TΔS.

Negative ΔG

Indicates a spontaneous, exergonic reaction.

Positive ΔG

Indicates a non-spontaneous, endergonic reaction.

Chi-square formula

χ² = Σ((O − E)² / E).

Observed value (O)

The actual measured data from an experiment.

Expected value (E)

The predicted or theoretical value.

Degrees of freedom

The number of categories minus one (n − 1).

Critical value

Used to determine if results are statistically significant.

Rejecting the null hypothesis

Occurs when χ² > critical value; results NOT due to chance.

Failing to reject the null hypothesis

Occurs when χ² < critical value; results are due to chance.

Null hypothesis (H0)

States that there is no difference, no effect, or differences are due to random chance.

Alternative hypothesis

States that there IS a difference or an effect.

Standard error

The standard deviation of the sample mean; measures accuracy.

Small standard error

Indicates consistent data and reliable mean.

Large standard error

Indicates variable data and less reliable mean.

Error bars

Graphical display of standard error on data points.

Overlapping error bars

Indicate no significant difference between groups.

Non-overlapping error bars

Indicate a statistically significant difference.

Scientific claim

A testable statement based on observations or data.

Evidence

Data or observations that support a claim.

Reasoning

Explanation connecting evidence to biological principles.

Connecting results to biology

Relating experimental outcomes to concepts like enzymes, diffusion, respiration, etc.