#### 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/108-probability-and-statistics/1062-qualitative-and-quantitative-statistics.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/108-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/108-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/108-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/159-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/159-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/108-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/108-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/108-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/108-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/108-probability-and-statistics/1043-conditional-probability.html#### Continuous Probability Distributions

If a random variable has a continuous probability distribution, then may take any value in an interval. The end points of the interval may be included or not. If denotes possible values of the random variable then means ' may take values greater than...

https://astarmathsandphysics.com/ib-maths-notes/108-probability-and-statistics/1044-continuous-probability-distributions.html#### Cumulative Frequency Curves

Cumulative frequency curves are useful statistical tools that provide a visual summarry of data and enable an easy calculation of the interquartile range. Suppose we have a data set comprising the lengths of a selection of fish, summarised in the table...

https://astarmathsandphysics.com/ib-maths-notes/108-probability-and-statistics/1046-cumulative-frequency-curves.html#### Discrete and Continuous Random Variables

A random variable represents the possible outcomes we could observe on measuring some quantity. Ransdom variables can be either discrete or contionuous. A discrete random variable has possible values The number of possible values that can take might be...

https://astarmathsandphysics.com/ib-maths-notes/108-probability-and-statistics/1047-discrete-and-continuous-random-variables.html#### Finding the Quartiles and Median of a List of Numbers

To find the median and quartiles of a list of numbers, first sort them – if they are not already sorted. If there are n numbers in the list: The median will be the th number . If this is not a data point – is even – find the averare of the th and th...

https://astarmathsandphysics.com/ib-maths-notes/108-probability-and-statistics/1048-finding-the-quartiles-and-median-of-a-list-of-numbers.html#### Finding the Mean From a Frequency Table

To find the mean of a list of numbers we add the numbers up and divide by how many numbers there are. For example the mean 1, 4, 6, 6, 7 is However sometimes we have a list in the form of a table. The table below is a fictitious summary of the number...

https://astarmathsandphysics.com/ib-maths-notes/108-probability-and-statistics/1049-finding-the-mean-from-a-frequency-table.html#### Histograms

A histogram is a type bar chart using intervals on the x -axis, with the modification that the interval sizes are not fixed. The frequencies are defined by the areas of the bars, and the y – axis is not a frequency axis, but a frequency density axis. A...

https://astarmathsandphysics.com/ib-maths-notes/108-probability-and-statistics/1050-histograms.html#### Independent Events

Tow events A and B are statisitically independent if neither influences the oother. The probability of event A occurring does not influence the probability of event B occurring and vice verse. Suppose neither event A or event B has occurred yet. Event...

https://astarmathsandphysics.com/ib-maths-notes/108-probability-and-statistics/1051-independent-events.html#### Introduction to 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/108-probability-and-statistics/1052-introduction-to-the-normal-distribution.html#### Mean and Variance of the Poisson Distribution

The Poisson distribution models events occurring at a constant average rate so that in each fixed time period we expect events to occur. The probability that events will occur in a single fixed time period is and the variance of the number of events in...

https://astarmathsandphysics.com/ib-maths-notes/108-probability-and-statistics/1053-mean-and-variance-of-the-poisson-distribution.html