Learning Lab

Download the measurement worksheets to improve your skills in these areas.

• 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.

• S4 Measures of spread

  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.