## Statistics

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.

- Statistics
- S1 Summation notation
- S2 Data
- S3 Mean, mode, median
- S4 Measures of spread
- S5 Probability rules
- S6 Sample spaces
- S7 Conditional probability
- S8 Binomial probability
- S9 Normal distributions
- S10 Standard normal distribution
- S11 Probability and the normal distribution
- S12 Sampling distributions
- S13 Confidence intervals
- S14 Hypothesis testing
- S15 T-tests
- S16 P-value
- S17 One sided tests
- S18 Tests of proportion
- S19 Poisson distribution