TOOL 3:  Mathematics

T3.1    Applying general mathematics

• Use basic arithmetic and algebraic calculations to solve problems 
• Carry out calculations involving: decimals, fractions, percentages, ratios, proportions, frequencies (including allele frequencies), densities, approximations and reciprocals 
• Calculate measures of central tendency: mean, median and mode 
• Apply measures of dispersion: range, standard deviation (SD), standard error (SE), interquartile range (IQR) 
• Use and interpret scientific notation (for example, 3.5 × 106)
• Use approximation and estimation 
• Calculate scales of magnification 
• Calculate rates of change from graphical or tabulated data
• Understand direct and inverse proportionality between variables, as well as positive and negative correlations between variables
• Calculate and interpret percentage change and percentage difference
• Distinguish between continuous and discrete variables
• Calculating the actual size from a micrograph that has a scale bar 
• Apply the Simpson reciprocal index
• Apply the Lincoln index
• Apply the chi-squared test.
  • Chi-Square independence 
  • Chi-square association
• Apply the t-test

T3.2    Using units, symbols and numerical values

• Apply and use International System of Units (SI) prefixes and units or non-SI metric units 
• Express quantities and uncertainties to an appropriate number of decimal places 

T3.3    Processing Uncertainties

• Understand the significance of uncertainties in raw and processed data
• Record uncertainties in measurements as a range (±) to an appropriate level of precision
• Express ranges, degrees of precision, standard error or standard deviations as error bars 
• Express measurement and processed uncertainties to an appropriate number of decimal places or level of precision
• Apply the coefficient of determination (R2) to evaluate the fit of a trend line
• Interpret values of the correlation coefficient (r) and identify correlations as positive or negative
• Apply and interpret appropriate tests of statistical significance (for example, chi-squared test)

T3.4    Graphing

• Sketch graphs, with labeled but unscaled axes, to qualitatively describe trends 
• Construct and interpret tables, charts and graphs for raw and processed data including bar charts, histograms, scatter graphs, line and curve graphs, logarithmic graphs, pie charts, and box-and-whisker plot  
• Plot linear and non-linear graphs showing the relationship between two variables with appropriate scales and axes
• Draw lines or curves of best fit
• Interpret features of graphs including gradient, changes in gradient, intercepts, maxima and minima
• Draw and interpret uncertainty/error bars
• Extrapolate and interpolate graphs
• Design dichotomous keys
• Represent energy flow in the form of food chains, food webs and pyramids of energy
• Represent familial genetic relationships using pedigree charts