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- Maths and statistics
- Statistics and probability
Binomial probability is used in various scenarios, like quality control and genetics. By understanding binomial probability, we can make informed predictions and decisions based on repeated experiments. Use this resource to learn how to apply the concepts of binomial probability. Binomial probability ("bi" meaning "two" and "nomos" meaning "parts") helps...
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- Maths and statistics
- Statistics and probability
If two events are not independent, then the outcome of one event can change the probability of the second event occurring. Understanding the connection between these helps us make better predictions and decisions based on specific situations. Use this resource to learn about the concept of conditional probability. Conditional probability...
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- Maths and statistics
- Statistics and probability
When we use the mean of a sample to estimate the mean of an entire population, we use confidence intervals to help us understand the precision of our estimates and how confident we can be about them. This tool is useful for making informed decisions based on sample data. Use...
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- Maths and statistics
- Statistics and probability
Data is everywhere. It drives many aspects of our day-to-day lives. Use this resource to learn about the different types of data and some ways of displaying it. Collecting and processing data To study the relationships between variables (a characteristic, number, or quantity that can be measured or counted), you...
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- Maths and statistics
- Statistics and probability
Hypothesis testing is used anywhere we conduct research to determine whether there is a relationship between variables. These days, hypothesis testing forms the basis of machine learning and data science, where it is used to validate models and make sure they reliably detect patterns and make predictions. Use this resource...
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- Maths and statistics
- Statistics and probability
The mean, mode, and median provide a single value that is typical of the data. These measures of central tendency help summarise large datasets, making it easier to understand the overall pattern. Understanding these concepts is essential for analysing and interpreting data effectively. Measures of central tendency The mean, median,...
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- Maths and statistics
- Statistics and probability
By looking at how data in a set is distributed, we can see how much the data varies. This helps us understand the data better and make good decisions based on it. Use this resource to learn about the measures of spread. The measure of spread shows how spread out...
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- Maths and statistics
- Statistics and probability
If data is normally distributed, it is represented by a bell-shaped curve. Normal distributions are common in nature and statistics, like heights or test scores. Understanding this distribution helps us make predictions and compare data from different sources easily. Graphical representations of data may look quite different. Many things that...
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- Maths and statistics
- Statistics and probability
One-tailed hypothesis tests are useful when you have a clear idea about the direction of an effect, such as testing if a new drug performs better than the standard treatment, whether a new fabric treatment increases the durability of a textile, or if a new alloy used for aircrafts is...
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- Maths and statistics
- Statistics and probability
As well as comparing the test statistic to a critical value, we can test hypotheses by comparing a p-value to the significance level, \(\alpha\). Understanding p-values helps us decide if our results are meaningful or just due to random chance. Use this resource to learn how to use p-values. In...
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- Maths and statistics
- Statistics and probability
The Poisson distribution deals with the number of random occurrences over a period of time or a given space, such as the number of people who enter a shop every hour or the number of flaws in a sheet of glass. It is very handy, well beyond applications in STEM....
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- Maths and statistics
- Statistics and probability
To find probabilities in normal distributions that aren't standard, we need to adjust the data to a common scale using \(z\)-scores. This allows us to find the likelihood of certain outcomes in a range of contexts, like identifying manufacturing tolerances, testing the tensile strength of new materials or calculating the...
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- Maths and statistics
- Statistics and probability
Probability rules help us understand how likely different outcomes are. They are applied in a range of ways, like risk assessment and modelling. Having a good understanding of these basics will help you to predict and make sense of different possibilities. When considering a set of all possible outcomes, an...
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- Maths and statistics
- Statistics and probability
A sample space lists of all the possible outcomes, giving a complete picture of the situation. Sample spaces form the foundation for calculating probabilities and making predictions about future events. Use this resource to learn some ways to represent a sample space. A sample space is a list or diagram...
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- Maths and statistics
- Statistics and probability
Sampling distributions help us understand the behaviour of sample statistics, like means or proportions, from different samples of the same population. By examining these distributions, we can see how sample results might vary and how close they are likely to be to the actual population value. This concept is important...
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- Maths and statistics
- Statistics and probability
A standard normal distribution helps us compare different datasets by converting them to a common scale using values called \(z\)-scores. Understanding standard normal distributions makes it easier to calculate probabilities and assess how individual data points relate to the average. Use this resource to learn how to analyse standard normal...
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- Maths and statistics
- Statistics and probability
You may have seen the Greek symbol sigma (\(\Sigma\)) used in maths, but what does it mean? It is a way to simply express long numbers, using something called summation notation. A good understanding of summation notation is important in statistics for calculating averages and sums. Use this resource to...
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- Maths and statistics
- Statistics and probability
T-tests help us understand if the differences we observe in data are due to random chance or if they're meaningful. They are commonly used in research to compare groups, like testing if a new teaching method improves scores more than the old one. Use this resource to learn how to...
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- Maths and statistics
- Statistics and probability
Rather than comparing a sample mean to a population mean, we can compare a sample proportion to a population proportion. These tests of proportion are used broadly, like for checking if a new fabric meets quality standards by having fewer defects or evaluating customer satisfaction levels for financial services. Use...
