#### 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#### Calculating 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#### Mode, Median and Mean

While the mode, median and mean are all measures of average, there are fundamental differences between them all: when you hear politicians splitting hairs, they are often splitting hairs over the difference between the average – mean – value, or the...

https://astarmathsandphysics.com/ib-maths-notes/probability-and-statistics/1054-mode-median-and-mean.html#### Introducing the Normal Distribution

The normal distribution is the most useful, adaptable, flexible, used statistical distribution there is. All other distributions are, in a sense, subsumed by it because of the Central Limit Theorem, which says that in some circumstances any statistical...

https://astarmathsandphysics.com/ib-maths-notes/probability-and-statistics/1052-introduction-to-the-normal-distribution.html#### More Calculations Involving The Normal Distribution - Finding Probabilities

Suppose we have a distribution We will find using the diagram on the left. This corresponds to a probability of 0.6915 hence Now we will find illustrated by the diagram on the left. Ignoring the minus sign we go to the normal distribution tables and...

https://astarmathsandphysics.com/ib-maths-notes/probability-and-statistics/1055-more-calculations-involving-the-normal-distribution-finding-probabilities.html#### Mutually Exclusive, Exhaustive, Independent Events Illustrated on Venn Diagrams

Mutually exclusive events are events that cannot both happen at the same time: You either like bovril or hate it. You either do what we say or you die! (George Bush's sentiment). We can illustrate mutually exclusive events A and B on a Venn diagram....

https://astarmathsandphysics.com/ib-maths-notes/probability-and-statistics/1056-mutually-exclusive-exhaustive-independent-events-illustrated-on-venn-diagrams.html#### How to Deal With Negative z Values When Using the Normal Distribution

The z transform for the normal distribution is written Thenormal distribution tables are used as below: a)Find a value of usinga given value of usingthe above formula, then going to the normal distribution tables tolook up a probability using this...

https://astarmathsandphysics.com/ib-maths-notes/probability-and-statistics/1057-how-to-deals-with-negative-z-values-when-using-the-normal-distribution.html#### Pascal's Triangle

Pascal's triangle provides a quick and easy way to calculate the coefficients of the binomial expansion, The entries in the table are calculated by adding the entties in each table immediately above to the left and right, with the exceptions of the...

https://astarmathsandphysics.com/ib-maths-notes/probability-and-statistics/1058-pascal-s-triangle.html#### Populations, Samples and Censuses

A population is the set of individuals in a group. Often information needs to be collected about the population, Taking a census and taking a sample are methods of collecting data about the population. A govenrnent for example needs to plan the supply...

https://astarmathsandphysics.com/ib-maths-notes/probability-and-statistics/1059-populations-samples-and-censuses.html#### Probability Mass Functions - Discrete Distributions

Every probability distribution has a probability density function, or probability mass function in the case of a discrete distribution, in terms of which it is usually defined. The probability density function for the normal distribution is for the...

https://astarmathsandphysics.com/ib-maths-notes/probability-and-statistics/1060-probability-density-functions-discrete-distributions.html#### Probability Tables

We start with a raw table of values and for each value, a probability of getting that value. x 1 2 3 4 5 P(X=x) 0.1 0.3 0.15 0.25 0.2 From this table we can find There are formulae for and They are Suppose we need to find and No matter how we transform...

https://astarmathsandphysics.com/ib-maths-notes/probability-and-statistics/1061-probability-tables.html#### Quartiles & Median From Frequency Tables

We start with the table below which summarises the daily sales in a newspaper shop over a year for the 360 days the shop was open. Sales Number of Days 1 -200 166 201- 400 100 401 - 700 59 701 - 1000 30 1001 -1500 3 To find the lower quartile we use...

https://astarmathsandphysics.com/ib-maths-notes/probability-and-statistics/1063-quartiles-and-median-from-frequency-tables.html#### Skewness

The normal distribution is symmetrical – small values are as likely as large values. The probability distribution for the normal distribution is symmetrical about the mean. This is not the case for most distributions however. Most probability...

https://astarmathsandphysics.com/ib-maths-notes/probability-and-statistics/1066-skewness.html#### Space Diagrams

A space diagram is a table which displays all the possible outcomes. They are usually used for discrete distributions and are especially useful when 2 or more trials are carried out simultaneously and the results must be combined in some way. For...

https://astarmathsandphysics.com/ib-maths-notes/probability-and-statistics/1067-space-diagrams.html#### Standard, Deviation, Variance and Bias

Given a flock of sheep, we can measure the masses of a sample of sheep and calculate the mean mass and the standard deviation of the masses of the sheep in the sample. Suppose the masses of the sheep are 50, 55, 52, 60, 54, 49, 59, 58 The sample mean...

https://astarmathsandphysics.com/ib-maths-notes/probability-and-statistics/1068-standard-deviation-variance-and-bias.html#### Summary of Formulae - Conditional Probability, Independent Events etc

This is only true if A and B are independent. You can never assume A and B are independent. You must either know it or prove it. This is always true for two events A and B. The left hand side P(A divides B) is the probability that A will happen given...

https://astarmathsandphysics.com/ib-maths-notes/probability-and-statistics/1069-summary-of-formulae-conditional-probability-independent-events-etc.html#### The Binomial Distribution

The name “The Binomial Distribution” is derived from the binomial expansion, because if you use the formula for binomial expansion, you can substitute and and then the probability of obtaining successes in attempts is given by the th term There are...

https://astarmathsandphysics.com/ib-maths-notes/probability-and-statistics/1070-the-binomial-distribution.html#### The Poisson Distribution

When events occur at a constant average rate, the distribution decribing the events can be modelled by a Poisson distrubtion. Examples include: Plane crashes Spelling or grammatical errors in a textbook School shootings (only in America) It is...

https://astarmathsandphysics.com/ib-maths-notes/probability-and-statistics/1071-the-poisson-distribution.html