Mathematics is fundamental to science
Numeracy is the ability to understand numbers and calculations. Science students rely on mathematics knowledge and skills when they undertake a scientific inquiry and communicate about their own and others’ ideas.
Glossary of maths terms useful for Investigating Science
Glossary created in Quizlet. You can practice the keywords.
General maths resources and guides
Here are links to useful websites that contain excellent guides, tutorials and examples that you can use to go over maths principles and skills.
- This PDF called the language-of-mathematics-in-science-guide-ase-2016-3- is aimed at teachers. However, students will find it very useful for Investigating science.
- Ducksters page for maths
- Maths is fun
- Khan Academy
- How to use your maths calculator. The instruction manual for the Casio Fx82AU type calculators.
Accuracy and precision in measurements
- accuracy and precision in measurements– definitions
- accuracy in precision using examples
- An excellent 20 min youtube video that discusses precision and accuracy, including definitions and examples. For the first 9 minutes, after it introduces significant figures which are mentioned below.
- a youtube video tutorial with more examples measuring volume, mass, length, and temperature with the correct number of digits
Uncertainty in measurements( higher level)
Error and limitations of data
Errors can affect the reliability and accuracy of the investigation results and therefore affect the overall validity of the investigation. Some can be avoided, like parallax error a type of random error), while others need to be carefully controlled when conducting the investigation.
- Parallax error
- Reliability and accuracy, in terms of both first hand and second-hand data.
- systematic and random error
- A straightforward youtube video on systematic and random error.
ERRORS CAN AFFECT THE ACCURACY AND PRECISION OF RESULTS. SEE WHAT THESE MEAN HERE.
Scientists use significant figures as a way to demonstrate the precision and accuracy of measurements taken during observations and experimentation.
- Rounding up numbers and decimals
- video on significant figures from 8 minutes onwards
- Which figures are significant? and more examples and questions
- Measurement and precision and significant figures and some practice questions
Scientists use scientific notation because they often deal with very large objects and distances such as those found when studying the universe and earth sciences or very tiny distances such as those found when they study the inside of an atom and microbiology.
- Powers of 10 what is that about?
- Scientific notation explained by Veritasium.
- converting numbers to scientific notation
- scientific notation practice
- Doing maths with scientific notation using a calculator
The following four dot points come from this link. There is also a great deal more detail that students should find useful as their studies progress.
- Bar/Column Graph: best for comparing data values such as height or weight. This graph is best used when analysing multiple samples or groups as it allows the reader to quickly and easily compare data values.
- Line Graph: best for demonstrating a change in data over time. A line graph can be used to track a single sample or can incorporate multiple lines to compare trends in change over time. This makes the line graph extremely versatile in its use and easily one of the most important graphs to master.
- Pie Chart: best for comparing percentages or fractions. In a pie chart, the circle (which represents the whole) is divided up into sectors to represent portions of the whole- the larger the sector, the bigger the portion. Great use of a pie chart would be to summarise a budget, a monetary one or even a metabolic budget.
- XY scatter plot: best for identifying trends between two different sets of data. A trend line is required to determine a correlation. One example would be latitude and the diameter of tree trunks.
Some terms you should know
discrete and continuous data notes and mini quiz
Line graphs and scatterplots
- When to use a line graph or a scatterplot
- Line graphs from the University of Western Sydney
- How do make a line graph in Excel ( Youtube video)
- A video guide on how to set up scatter plots using Excel.
Bar graphs and histograms
- Bar graph or histogram?
- bar graphs
- How do make a line graph in Excel ( Youtube video)
- Using excel to draw a bar chart( video tutorial)
The relationship between variables
Science uses mathematics to explain the relationship between the data and variables in an investigation. The following link introduces what this is all about. It also includes some excellent questions and answers, that you should feel more confident answering as you complete more of this course.
Tools for determining accuracy and precision
Scatter plots- looking for correlations( relationships)
Scatter plots are produced when plotting continuous data on both the x and y variable. Once the data points are graphed, a correlation may be evident in the data. Investigations that that collect a lot of data will produce scatter plots that are more likely to give a more reliable interpretation of correlation.
A tutorial and lesson from c-K12. It contains introductory to advanced information. You do not need to be able to do the mathematics; however, you should understand what the pattern shows and what the value of r means.
- A video guide on how to set up scatter plots using excel.
- Using graphs and learning about the line of best fit- this example comes from a geoscience page. However, there is useful information regarding scatterplots.
Statistics with scatterplots
- A video guide on how to use excel to calculate the correlation coefficient. This number labelled as “r” shows the likelihood of a relationship between the independent (x) and dependent (y) variable.
- The following link describes what the value of “r” means.
Limitations of correlations
Correlations are not good at interpreting curved patterns of data. Correlations are also not always causations. That is just because there is a strong correlation does not mean that one is the cause of the other.
Describing relationships in line graphs
When the results of an investigation are graphed, it shows a relationship between two variables. When investigating the Laws of science, there are often specific relationships that can be observed when graphing results.
Linear – a straight-line relationship between variables but it is not always directly proportional( see below). The gradient(m) or slope is used to identify the rate of change. Thes can be described as positive, negative and no change or zero and undefined.
You can use the line if best fit to determine whether you have some sort of linear relationship. The line of best fit is improved by having more experimental data.
Directly proportional- when one value increases the other value increases by the same amount. Note the line is straight and always goes through the 0,0 origin.
Inversely proportional- one value decreases at the same rate as the other increases. This is seen as a curved line.
Standard deviation – testing precision
The statistic that measures this spread is called the standard deviation. The wider the spread of scores, the larger the standard deviation.
Standard Deviation – Explained and Visualized ( vid)
- Calculating standard deviation( vid)
- Standard deviation online calculator
- Standard deviation and variance
- precision and standard deviation- more detailed
Graphing and calculating means and standard deviations using Excel
Using Excel is fairly easy and a much faster way to graph and calculate basic statistics for data created during investigations.
- How to calculate mean and standard deviation in excel ( video tutorial)
- Adding standard deviation error bars in excel (video tutorial)
- standard deviation information, including tutorials on how to calculate this and use google or excel to do so.
Other types of graphical analysis
1. Box and whisker plots- looking at the level of variability in the data
What information is in box and whisker plots? A box and whisker plot—also called a box plot—displays the five-number summary of a set of data. The five-number summary is the minimum, first quartile, median, third quartile, and maximum. In a box plot, we draw a box from the first quartile to the third quartile. A vertical line goes through the box at the median. The whiskers go from each quartile to the minimum or maximum.
2. Error bars – looking for a statistically significant difference between one bar and another.
An error bar is a line through a point on a graph, parallel to one of the axes, which represents the uncertainty or variation of the corresponding coordinate of the point. In IB Biology, the error bars most often represent the standard deviation of a dataset. You can plot your error bars in Excel. Use the link to see how to do this.
Investigations with populations: Sample size, reducing Bias and improving and reliability
The more data that is collected, without error, the more reliable the observation. However, it may be challenging to determine the sample size required for each investigation. The following links may help you in making this decision.
- What is the meaning of sample size?
- Determining sample size
- more to add here…
- Randomised clinical trials and epidemiological studies and their limitations a Ted-ed video
Statistical methods in Science
While it is beyond the scope of this course to have you actually apply more complex statistics to your own work, you will be expected to at least become familiar with the type of commonly used tests in science. This is especially relevant when you start to read scientific papers. Students completing a higher level of mathematics will obviously have an advantage when studying science, especially at a tertiary level.
The following are some links that should help you.