 ## Statistics

• 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 in the formulas for statistical calculations.

• 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 the spread of a set of data.

• 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 distribution

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

• 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 can be found via a calculator or a “z-table”.

• 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-test

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.

• 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 greater than (or alternatively, less than) the population mean.

• S19 Poisson distribution

The Poission 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.

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