#### What is a Statistic?

A statistic is a single measure of some attribute of a sample e.g.the mean. It is calculated by applying a function to the set of data. More formally, statistical theory defines a statistic as afunction of a sample where the function itself is...

https://astarmathsandphysics.com/a-level-maths-notes/s2/3775-what-is-a-statistic.html#### Qualitative and Quantitative Statistics

Statistical data comes in one ogf two broad types Qualitative and Quantitative. Qualitative data is descriptive – a colour, type or one of a category. The categories that describe qualitative data may be ordered or not. We may order colours in order of...

https://astarmathsandphysics.com/ib-maths-notes/probability-and-statistics/1062-qualitative-and-quantitative-statistics.html#### Misleading Statistics

Of course, drawing that strict statistical inference is ridiculous, and illustrates that you must be careful when using statistics, especially since so much discussion statistical discussion tends to get tied up in wordplay. Probably the best examples...

https://astarmathsandphysics.com/a-level-maths-notes/s1/3716-misleading-statistics.html#### A Level Maths Notes - Statistical/Reference Tables

https://astarmathsandphysics.com/a-level-maths-notes/statistical-reference-tables.html#### Statistical Models and Modelling

All statistically models assume randomness. Not complete randomness, so that all possible outcomes are equally likely, but a randomness that makes some outcomes more or less likely. We have to model each situation so that the predictions of the model...

https://astarmathsandphysics.com/a-level-maths-notes/s1/3737-statistical-models-and-modelling.html#### IB Maths Notes - Probability and Statistics

https://astarmathsandphysics.com/ib-maths-notes/probability-and-statistics.html#### University Maths Notes - Probability and Statistics

https://astarmathsandphysics.com/university-maths-notes/probability-and-statistics.html#### Qualitative and Quantitative Statistics

Statistical data comes in one ogf two broad types Qualitative and Quantitative. Qualitative data is descriptive – a colour, type or one of a category. The categories that describe qualitative data may be ordered or not. We may order colours in order of...

https://astarmathsandphysics.com/a-level-maths-notes/s1/3728-qualitative-and-quantitative-statistics.html#### Formulae Used in Statistics

https://astarmathsandphysics.com/university-maths-notes/probability-and-statistics/2024-formulae-used-in-statics.html#### Hypothesis Testing Using Test Statistics or Using Probabilities

There are two ways we can conduct a hypothesis test. Iwill illustrate with an example from the normal distribution assuminga two tailed test. Using a Test Statistic We have a null distribution anda single observation We find Supposewe are conducting a...

https://astarmathsandphysics.com/a-level-maths-notes/s2/3756-hypothesis-testing-using-test-statistics-or-using-probabilities.html#### Regression Lines

The correlation coefficient can be found if necessary to found how good a relationship we have. You may be given summary statistics etc but I will illustrate an example from scratch. Example: Find the equation of the regression line of height above...

https://astarmathsandphysics.com/ib-maths-notes/probability-and-statistics/1064-regression-lines.html#### Simultaneous Equations Problems Involving the Normal Distribution

set of data and so cannot find the mean and standard deviation from a set of readings. However, given JUST TWO suitable statistics we can find the mean and standard deviation of a list. This is because there are two constants we must find, and any set...

https://astarmathsandphysics.com/ib-maths-notes/probability-and-statistics/1065-simultaneous-equations-problems-involving-the-normal-distribution.html#### The Correlatioin Coefficient

table. x 2 4 7 3 5 1 y 10 5 2 9 4 10 To find the correlation coefficient it is most efficient to first find the summary statistics. Your calculator may have functions to help. They are The correlation coefficient is then calculated from r= This means...

https://astarmathsandphysics.com/ib-maths-notes/probability-and-statistics/1045-the-correlatioin-coefficient.html#### Control Charts

Control charts are much used in quality control to track statistics such and the mean and standard deviation in a production process. They consist of points representing a statistic being tracked plotted against time. The mean of this statistic – the...

https://astarmathsandphysics.com/university-maths-notes/probability-and-statistics/2022-control-charts.html#### Proof of Central Limit Theorem

The cenral limit theorem is one of the most important theorems in statistics. It approximates the distribution of the mean of any sample of size n from any distribution by the distribution Now write so we have Now expand so since Taking the Fourier...

https://astarmathsandphysics.com/university-maths-notes/probability-and-statistics/2030-proof-of-central-limit-theorem.html#### Advanced Questions on Venn Diagrams

More complicated question on Venn diagrams involve the use of simultaneous equations, or the introduction of a dummy variable x. Example Sketch the Venn diagram. (1) (2) Divide (1) by (2) to get Substitute these into the equation Then and from (1) We...

https://astarmathsandphysics.com/ib-maths-notes/probability-and-statistics/1039-advanced-questions-on-venn-diagrams.html#### Bayes' Theorem

Suppose we observe a random variable and wish to make inferences about another random variable where is drawn from some distribution From the definition of conditional probability, Again from the definition of conditional probability, we can express...

https://astarmathsandphysics.com/ib-maths-notes/probability-and-statistics/1040-bayes-theorem.html#### Boxplots or Box and Whisker Diagrams

A box-and-whisker plot or boxplot is a visual display of some of the five figure summary of a data set. It shows the minimum value, the lower quartile the median the upper quartile and the maximum value For the data set 2, 4, 4, 6, 7, 8, 12, 13, 17,...

https://astarmathsandphysics.com/ib-maths-notes/probability-and-statistics/1041-boxplots-or-box-and-whisker-diagrams.html#### Calculations Involving The Normal Distribution - Finding Probabilities

If you look at the tables for the normal distribution, along the top and left borders there are z – values. If we have a Normal distribution and we want to find then we can use the – transform to find a – value then find the probability for this –...

https://astarmathsandphysics.com/ib-maths-notes/probability-and-statistics/1042-calculations-involving-the-normal-distribution-finding-probabilities.html#### Conditional Probability

Conditional probability questions arise when two possibly linked events, and occur. We ask, given that has happened, what is the probability that will happen? The equation we use is, the meaning of which is illustrated in the diagram below. What we are...

https://astarmathsandphysics.com/ib-maths-notes/probability-and-statistics/1043-conditional-probability.html