 Statistics

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S1 Summation notation

Summation notation, also known as 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 that is often used...

S10 Standard normal distribution

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...

S11 Probability and the normal distribution

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.

S12 Sampling distributions

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.

S13 Confidence intervals

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.

S14 Hypothesis testing

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.

S15 T-tests

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”...

S16 P-value

Hypotheses can be tested by comparing the test statistic to the critical value or by comparing the p-value to the significance level, α.

S17 One sided tests

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.

S18 Tests of proportion

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...

S19 Poisson distribution

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...

S2 Data

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.

S3 Mean, mode, median

The mean, the median and the mode are three different measures of central tendency. This module shows the three different ways in which you can find a single number to summarise a set of data.

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...

S5 Probability rules

This module covers the rules of basic probability, including the multiplication and addition principles and complementary events.

S6 Sample spaces

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.

S7 Conditional probability

If two events are not independent then the outcome of one event can change the probability of the second event occurring.

S8 Binomial probability

The binomial distribution is a discrete distribution consisting of repeated trials, where each trial has two possible outcomes.

S9 Normal distributions

The normal distribution is a “bell-shaped”, symmetrical, continuous probability distribution.

Statistics

Statistics booklets and worksheets