Maths and Statistics
|Site:||Solent Online Learning|
|Book:||Maths and Statistics|
|Printed by:||Guest user|
|Date:||Saturday, 22 September 2018, 6:50 AM|
Table of contents
- Improving your Numeracy
- Introductory Maths
- Shapes and Area
- Angles and Geometry
- Introductory Statistics
- Statistics Foundations: Part 1
- Statistics Foundations: Part 2
- Statistics with Excel: Part 1
- Statistics with Excel: Part 2
- Introduction to SPSS
- SPSS Statistics Essential Training
- More Help
- Extra resources
Improving your Numeracy
Do you feel you have forgotten your maths since leaving school? Do you worry about numbers and whether you can cope with the university course you have chosen?
Would you like to:
- regain your numerical confidence?
- practice your basic skills?
You may also find the Numeracy Refresher booklet useful to refresh your knowledge on the following topics:
The BBC Bitesize website is primarily aimed at school children but is also very useful as a revision tool for basic skills. Suitable for foundation and first year students transitioning into university, it provides you with a refresher on a range of numeracy topics including:
- place value
- distance, speed and time
- rounding and estimating
- ratio and proportion
- prime numbers, factors and multiples
- powers and roots
- positive and negative numbers
- operations (calculations/sums)
- looking after your finances
- standard index form
There is currently a bewildering array of online support offering mathematical support. Some of this support is excellent; some of it not so helpful.
The BBC Skillswise website is a good starting point for foundation skills and revision. It offers "practical, commonsense maths for adults":
- practising mental maths
- understanding decimals and fractions
- working with percentages and ratios
- solving equations
- calculating area and volume
- scaling recipes
- estimating your running speed
- calculating the area for home improvement projects
- working with probability
Addition and subtraction
Straightforward addition and subtraction are foundation skills you will have mastered before coming to university. Dee Greig-Dunn, Lecturer in Mathematics and Meteorology at Solent University, offers you some useful tips around adding and subtracting positive and negative numbers, building on your basic skills.
Watch Dee Greig-Dunn explain how you can add and subtract positive and negative numbers using number lines:
Multiplication and Division
There are a few basic rules to remember when multiplying and dividing positive and negative numbers. Take a look at the video (below) in which Dee Greig-Dunn, Lecturer in Mathematics and Meteorology at Solent University, explains these foundation skills and the basic rules you need to remember.
How to multiply and divide positive and negative numbers.
When both numbers are the same (two positive or two negative numbers) the answer will always be positive.
When both numbers are different (one positive number and one negative number), the answer will always be negative.
BIDMAS and BODMAS
BIDMAS (also known as BODMAS) helps you to remember the order that you need to do your mathematical calculations where there is more than one mathematical operator (any combination of brackets, indices, division, multiplication, addition, subtraction).
This easily remembered acronym stands for:
I ndices (powers of)
Take a look at the video (below) in which Dee Greig-Dunn, Lecturer in Mathematics and Meteorology at Solent University, explains how to apply BIDMAS (BODMAS) to the following calculation:
(3 + 4)² - 7 + 4 × 3
On your calculator you will often need to round up numbers with lots of decimal places to an appropriate level of accuracy.
In the video (below) Dee Greig-Dunn, Lecturer in Mathematics and Meteorology at Solent University, explains:
- how to round up to one, two and three decimal places
- how to round up to a specified number of significant figures
A ratio shows the relationship between two numbers and demonstrates how many times the first number contains the second.
In the videos (below) Dee Greig-Dunn, Lecturer in Mathematics and Meteorology at Solent University, demonstrates:
- what you need to do in order to share a sum of money or a weight in a particular ratio (video 1)
- how to deal with problems where you are required to scale ratios (video 2)
I would like to mix paint and white spirit in the ratio 5:2.
How much white spirit is needed to thin 25 litres of paint?
How much white spirit (WS) will be required?
I would like to make cocktails by mixing whisky and vodka in the ratio 3:2. I only have 5 litres of each spirit.
How much cocktail can I make?
Substitution by integration
As a first year undergraduate student you may have come across substitution by integration (a part of calculus).
In the video (below), Dr Janet Bonar (Course Leader in the School of Maritime Science and Engineering) demonstrates a step by step approach to solving the following problem:
cos(3 + 1) d, using the substitution u= 3 + 1
Step 2 Guess a likely substitution. If there are brackets, this is often the bit inside the brackets. Take the derivative of the substitution. If the derivative term is in the original equation, then substitution is the right technique. In particular, the variable should be in your derivative, and to the same power, as in the other part of your original equation.
Step 3 To do the substitution, solve your derivative term for d
Step 4 Substitute your u term and your d term into the original equation and cancel where you can.
Now you can see why it's called 'substitution'!
Step 5 Integrate your new, simple equation. It should be much easier!
Step 6 Write the solution, don’t forget to include the constant of integration.
Step 7 Substitute the original variable back in—and you’re done!
Now watch how Dr Janet Bonar works through the steps in this video:
For an introduction to everyday algebra fundamentals, go to:
Algebra topics include:
- completing the square
- expanding, or removing, brackets
- mathematical language
- partial fractions
- Pascal's triangle and the binomial expansion
- polynomial division
- powers or indices
- simple linear equations
- simplifying algebraic fractions
- simultaneous linear equations
- solution of linear and quadratic inequalities
- solving cubic, polynomial and quadratic equations
- substitution and formulae
- transposition of formulae
To better understand the graphs topic, spend time refreshing your knowledge on key areas such as:
- plotting graphs
- straight line graphs and gradients
- travel graphs
- conversion graphs
- real-life graphs
- quadratic graphs
Downloadable resources on the following topics include:
- line graphs
- double charts
- split tables
- bar charts
- composite bar charts
- pie charts
Shapes and Area
To better understand the shapes and areas topics, spend time refreshing your knowledge on key areas such as:
- the properties of 2D and 3D shapes
- volumes and nets
- perimeters and areas
- perimeter, area, volume
- Pythagoras theorem
Angles and Geometry
To better understand the angles and geometry topics, spend time refreshing your knowledge on key areas such as:
- lines and angles
- measuring and drawing
- Pythagoras's theorem
For an introduction to geometry take a look at:Topics included are:
- co-ordinate geometry of a circle
- equation of a straight line including gradient and intercept
- Euclidean geometry
- other conic sections (ellipse, hyperbola, parabola)
- polar co-ordinates
- properties of straight line segments
- the gradient of a straight line segment
The BBC Bitesize website is suitable for foundation and first year students transitioning into university. It also provides you with a refresher on a range of angles and geometry topics.
To better understand the measures topics, spend time refreshing your knowledge on key areas such as:
- units and converting units
- reading scales
- rounding and estimating
- reading timetables
- compass directions and maps
If you are an engineering student, for example, you may have come across units that are not in the International System of Units (SI).
The BBC Bitesize website is suitable for foundation and first year students transitioning into university.
As you enter the world of work, you will find that most jobs use statistics of some kind.
Once you understand the foundations, you will begin to understand how statistics can not only be used, but also abused, in order to influence social policy
For example, the link below explores how foreign secretary, Boris Johnson, is accused of mis-using official statistics for political gain, and considers whether the leader of the Labour Party, Jeremy Corbyn, is correct to say that there are fewer students from disadvantaged backgrounds going to university now.
But first of all, you need to be comfortable with the terms, formulas and techniques that are needed to use statistics.
To better understand the statistics and probability topics, spend time refreshing your knowledge on key areas such as:
- collection data
- mean, median and mode and range of data
- charts and graphs
- frequency tables
The following websites are a useful source of further information:
Understanding the use of statistics-the law
Understanding how statistics are used in your particular subject field is important too.
The Royal Statistical Society with the Inns of Court College of Advocacy have released a guide which helps understanding in the use of statistical evidence in courts and tribunals.
Whilst the guide is aimed at advocates it could also be of use to law students:
More detailed guides on criminal law and statistics available from:
Statistics Foundations: Part 1
- Why statistics matter
- Evaluating your data sets
- Finding means, medians, and modes
- Calculating standard deviation
- Measuring distribution and relative position
- Understanding probability and multiple-event probability
- Describing permutations: the order of things
- Calculating discrete and continuous probability distributions
Statistics Foundations: Part 2
As a follow on to Statistics Foundations: Part 1, Professor Eddie Davila reviews introductory concepts such as data and probability. If you are looking to work in data science, business, and business analytics—or just need a deeper understanding of how statistics work in the real world- this video (below) is for you.
- Data and distributions
- Sample size considerations
- Random sampling
- Confidence intervals
- Hypothesis testing
Statistics with Excel: Part 1
If you need help with understanding statistics with Excel, then the video (below) is for you. In it, Joseph Schmuller explains the fundamental concepts of descriptive and inferential statistics and shows you how to apply them using Microsoft Excel.
- Understanding data types and variables
- Calculating probability
- Understanding mean, median, and mode
- Calculating variability
- Organising and graphing distributions
- Sampling distributions
- Making estimations
- Testing hypothesis: mean testing, z- and t-testing, and more
- Analysing variance
- Performing repeated measure testing
- Understanding correlation and regression
Statistics with Excel: Part 2
This video shows you how to use statistical concepts and tools to perform analysis in Microsoft Excel.
It would be useful to look at Statistics with Excel: Part 1 (on the previous page) if you are unsure of the basics. By watching both videos, you should have the necessary knowledge to perform basic analysis in workplace situations.
- Using Excel's statistical functions and 3D charts
- Visualising sampling distributions
- Performing comparisions with ANOVA
- Performing two-way analysis with ANOVA
- Analysing linear regression
- Performing multiple regression and non-linear regression analysis
- Making advanced correlations
- Testing variable frequencies
- Running simulations
Introduction to SPSS
What is SPSS?
"SPSS is a comprehensive system for analyzing data. SPSS can take data from almost any type of file and use them
to generate tabulated reports, charts, and plots of distributions and trends, descriptive statistics, and complex
statistical analysis." (SPSS Base User's Guide)
SPSS is the acronym of Statistical Package for the Social Sciences. It is a popular statistical package which can perform highly complex data manipulation and analysis with simple instructions. It is designed for both interactive and non-interactive (batch) uses.
Watch the SPSS Statistics essential training for more information.
SPSS Statistics Essential Training
If you want to make the most of the data you have collected for your academic assignments, then watch the video link below.The skills covered in the video are ideal for your research projects.
The video will help you to:
- build charts, scatterplots, and box plots
- calculate descriptive statistics such as means and standard deviations
- use inferential statistics such as t-tests and chi-squares
- enter and read data
- create new variables and crosstabulations
- model associations with correlations, contingency tables, and multiple-regression analysis
- format and export presentations to share your data
- Ask your lecturer for guidance.
- If you are a disabled student you can also contact Access Solent for guidance and support.
- View the glossary to help you understand the words used in Maths and Statistics.
- Read a book or ebook from the reading list found in Extra resources.
- Visit recommended websites in Extra resources for further guidance on Maths and Statistics.
Thank you to all staff and students at Southampton Solent University who contributed to this course.
Facts and formulae
This Functional Mathematics leaflet provides you with an at-a-glance list of facts and formulae to help you transition from school mathematics to university mathematics.
Have it beside you at all times!
Numerical reasoning support
The following leaflets (created for SIGMA by Dr E Lingham) will quickly and effectively refresh your knowledge on a range of topics that often arise in numerical reasoning tests including:
- bar charts
- shares and dividends
- foreign exchange
Download leaflets on the following topics which arise in numerical reasoning tests:
1. Lynda.com at Solent University (What is Lynda.com?)
The links below will take you directly to the course via Solent's institutional authentication on the SOL Lynda page:
3. Graduate numerical assessment
4. Useful maths support resources at other universities.
5. Online learning
There are a lot of online tools available to help you educate yourself. Khan Academy, FutureLearn and OpenLearn are useful starting points. For example, FutureLearn provides the following useful courses:
6. Maths anxiety
7. Use of Software