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Arithmetic and measurement Algebra Geometry and linear algebra Functions and graphs Calculus Statistics This glossary of maths symbols explains common notations you might encounter in the Learning Lab....
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Summation notation or sigma notation is a shorthand method of writing the sum or addition of a string of similar terms. This module explains the use of this notation. The basic idea We use the Greek symbol sigma \(\Sigma\) to denote summation. \(\Sigma\) is called the summation sign. A typical...
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A normal distribution with a mean of zero and a standard deviation of one is called the standard normal distribution. Areas under the standard normal distribution curve represent probabilities which can be found via a calculator or a “z-table”. The standard normal distribution (sometimes called a z-distribution) has a mean...
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In any normal distribution the mean and standard deviation can be used to convert it to a standard normal distribution and when can then compute probabilities. Even when data follows a normal distribution, different data sets will have their own mean and standard deviation and a different bell shaped curve...
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Learn how we can sample distributions. The distribution of the means of all the possible samples of a certain size tend to follow a normal distribution. A sampling distribution is the probability distribution for the means of all samples of size \(n\) from a given population. The sampling distribution will...
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We can use the mean of a sample to estimate the mean of the entire population. It is more appropriate to give an interval estimate rather than a point estimate. We use the statistics we obtain from samples to make inferences or estimates about the population from which the sample...
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This module explains how to set up and test hypotheses to see if a difference between a sample mean and a population mean is significant. Consider statements such as Teenagers aged \(13\)-\(15\) spend no more than \(10\) hours a week on Facebook. The average weight of Australian men is the...
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Hypothesis testing usually uses the population standard deviation to calculate a “z” value. If the population standard deviation is unknown, we use the sample standard deviation to calculate a “t” value. T-distribution In conducting a hypothesis test the population standard deviation \(\sigma\) may be unknown. In that case we approximate...
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Hypotheses can be tested by comparing the test statistic to the critical value or by comparing the p-value to the significance level, α. In hypothesis testing two approaches are possible when making the decision as to whether to reject the null hypothesis. So far we have compared the test statistic...
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How do we apply a test of proportions? Rather than comparing a sample mean to a population mean, we can compare a sample proportion to a population proportion. In the hypothesis tests we have looked at so far, we have been concerned to find evidence that there has been a...
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Hypothesis tests can be either two-tailed (non-directional) suggesting that the sample mean is different to the population mean, or one- tailed (directional) suggesting that the sample mean is greater than (or alternatively, less than) the population mean. A test of proportion is used to determine whether or not a sample...
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The Poisson distribution deals with the number of random occurrences over a period of time (or distance or area or volume), such as the number of people who enter a shop every hour, or the number of flaws in a sheet of glass. The Poisson distribution is a discrete distribution...
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Data is everywhere and increasingly drives many aspects of our day-to-day lives. Here we explain the different types of data that can be collected and some ways of illustrating this data. Definitions \(\mathbf{Population}\): the total group of individuals or items under consideration. \(\mathbf{Sample}\): a group of individuals or items chosen...
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The mean, mode and median are measures of the centre or middle of a set of data. They are sometimes called measures of central tendency and they provide a single value that is typical of the data. Definitions The mode is the value that occurs most often. The median is...
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The range, the interquartile range and the standard deviation are three different measures of the spread of a set of data. This module shows three different ways to calculate a number to represent the spread of a set of data. Measuring spread or dispersion in data Consider the two sets...
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This module covers the rules of basic probability, including the multiplication and addition principles and complementary events. The probability of an event \(A\) is expressed as a number between zero and one: \(0\leq Pr(A)\leq1\) . \(Pr(A)=0\) means that event \(A\) is impossible. \(Pr(A)=1\) means that event \(A\) is certain. When...
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A sample space is a list of all the possible outcomes. There are a number of techniques that can be used to list the sample space. A list or diagram showing all possible outcomes in a probability experiment is called a sample space. The probability that an event \(E\) occurs...
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If two events are not independent then the outcome of one event can change the probability of the second event occurring. Dependent events Two events are dependent if the outcome or occurrence of the first affects the outcome or occurrence of the second so that the probability is changed. Example...
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The binomial distribution is a discrete distribution consisting of repeated trials, where each trial has two possible outcomes. Introduction A random variable may be described as having a binomial distribution when there are a number of repeated trials and there are only two possible outcomes on each trial. The following...
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This module introduces the normal distribution. Data that is normally distributed is characterized by a bell shaped curve when displayed graphically. Graphical representations of data may look quite different as shown below: But many things that can be measured, such as heights of people blood pressure errors in measurement scores...
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Do you need to brush up on statistics or learn some new skills? The links on this page lead to Learning Lab pages that will put you on the right track. S1 Summation notation Summation notation, also known as sigma notation, is a shorthand method of writing the sum or...
