• The Standardized Score

    The standardized score is a statistical tool thatallows comparison of related quantities that are normallydistributed. A very good use is test scores. When a student wishes tocompare their own results with everybody elses, they may stanaridizetheir...

    https://astarmathsandphysics.com/ib-maths-notes/probability-and-statistics/1072-the-standardized-score.html

  • Venn Diagram For Three Independent Events

    If three events A, B and C are mutually independent, then Suppose that and then The Venn diagram starts as This includes the probability so subtract this to obtain the diagram below. Similarly for A and C and B and c respectively. Subtract to get 0.036...

    https://astarmathsandphysics.com/ib-maths-notes/probability-and-statistics/1073-venn-diagram-for-three-independent-events.html

  • Venn Diagrams 1

    Venn diagrams are a means to display categories of data graphically. They are more flexible than contingency tables, allowing complex reasoning, and have many applications in set theory. Typically each set is illustrated by a bubble, allowing...

    https://astarmathsandphysics.com/ib-maths-notes/probability-and-statistics/1074-venn-diagrams-1.html

  • Venn Diagrams 2

    Calculations involving Venn diagrams use the formulae: and if the events and are independent, where for example, P(A) indicates the probability of A happening. The best way to illustrate the use of these examples is by way of examples. A Venn diagram...

    https://astarmathsandphysics.com/ib-maths-notes/probability-and-statistics/1075-venn-diagrams-2.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/probability-and-statistics/1053-mean-and-variance-of-the-poisson-distribution.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/probability-and-statistics/1051-independent-events.html

  • Drawing 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/probability-and-statistics/1050-histograms.html

  • Finding the Mean From Frequency Tables

    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/probability-and-statistics/1049-finding-the-mean-from-a-frequency-table.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/probability-and-statistics/1048-finding-the-quartiles-and-median-of-a-list-of-numbers.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/probability-and-statistics/1047-discrete-and-continuous-random-variables.html

  • Cumulative Frequency Curves

    Length ( x mm) Frequency 2 4 8 14 6 4 2 We find the cumulative frequencies by adding up the frequencies as we go down the table. Length ( x mm) Cumulative Frequency 2 6 14 28 34 38 40 Cumulative frequency curves are useful statistical tools that...

    https://astarmathsandphysics.com/ib-maths-notes/probability-and-statistics/1046-cumulative-frequency-curves.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/probability-and-statistics/1044-continuous-probability-distributions.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

  • 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

  • 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

  • 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

  • Advanced Questions - 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

  • Poisson Cumulative Distribution Tables

    The table below gives the probability of that a Poisson random variable X with mean = λ is less than or equal to x. x\λ 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.2 1.4 1.6 1.8 0 0.9048 0.8187 0.7408 0.6703 0.6065 0.5488 0.4966 0.4493 0.4066 0.3679...

    https://astarmathsandphysics.com/a-level-maths-notes/statistical-reference-tables/3828-poisson-cumulative-distribution-tables.html

  • KS2 Science Tuition in London

    Pupils aged between seven and eleven are studying key stage 2. Pupils study a wide range of subjects: Art and Design Design and Technology English Geography History ICT Languages Maths Music PE Science Religious Education Our tutors teach science at...

    https://astarmathsandphysics.com/physics/ks2-tuition.html

  • Degree Level Maths Tuition From Maths and Physics Specialists

    Logic Matrices and Linear Algebra Metric Spaces Non Euclidean Geometry Number Theory Numerical Methods Probability and Statistics Set Theory Stochastic Processes Tensors Topology Vector Calculus Many topics cross boundaries. Other topics may be covered....

    https://astarmathsandphysics.com/maths/degree-level-tuition.html

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