Numeracy for Science

Mathematics is fundamental to science 

Quanta_TA.jpg
source

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 great guides, tutorials and examples that you can use to go over maths principles and skills.

Measurement skills 

Accuracy and precision in measurements 

accuracy
Accuracy is determined by dividing the smallest division in the scale by 10. The most precise measurement is the lowest. Image sourced from this youtube video.

 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.

 

maxresdefault.jpg
From youtube video above.

ERRORS CAN AFFECT THE ACCURACY AND PRECISION OF RESULTS. SEE WHAT THESE MEAN HERE.

Significant figures

Scientists use significant figures as a way to demonstrate the precision and accuracy of measurements taken during observations and experimentation.

Scientific notation

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.

This awesome video shows you the sales of the universe in powers of 10.

prefixes
Image source and  lesson

Representing data-Graphing 

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 analyzing 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. A great use of a pie chart would be to summarize 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

image.png
source

Bar graphs and histograms

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.

correlation.png
Scatter plots, what do they show?

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.

Chart-Tiff-copy.png
image source

you-dont-say-memes-com-14014390

Non- linear relationships 

 

 

 

 

 

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.

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.

Other types of graphical analysis 

1. Box an 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.

box_plot
Image source 

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.

error bars
source

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 difficult to determine the sample size required for each investigation. The following links may help you in making this decision.

 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 a greater advantage when studying science.

The following are some links that should help you.