• Hypothesis Testing With the Binomial Distribution

    If a manufacturer claims superiority for any of their products or a great deal rests the proportion of components that exceed a certain lifetime, then that claim or proportion probably needs to be tested for legitimacy or accuracy. We can test a wide...

    https://astarmathsandphysics.com/a-level-maths-notes/s1/3711-hypothesis-testing-with-the-binomial-distribution.html
  • Outliers

    An outlier of a statistical sample is an extreme value – the very rich man, the dwarf, the Spruce Goose – a large plane built by reclusive billionaire Howard Hughes. It flew only once and now sits in a museum – a monument to people with too much money....

    https://astarmathsandphysics.com/a-level-maths-notes/s1/3721-outliers.html
  • The Central Limit Theorem

    Suppose we have a list of measurements of some quantity from some population. We don't know the underlying distribution, but for some purposes this does not matter. If we are only interested in analysing the mean of the list, there is a very useful...

    https://astarmathsandphysics.com/a-level-maths-notes/s1/3740-the-central-limit-theorem.html
  • Prediction and Extrapolation

    Extrapolationis a bad idea. It involves using a set of data to make predictionsfor data outside the range used to construct a statistical model.Suppose for example that a drug is being tested. The drug is designedto lower cholesterol. The drug is...

    https://astarmathsandphysics.com/a-level-maths-notes/s2/3763-prediction-and-extrapolation.html
  • Type I and Type Errors - The Power of a Test

    Conducting a hypothesis test is by nature an uncertainbusiness. Just be cause you do not reject the null hypothesis, itdoes not mean that the null hypothesis is true. There is in factinsufficient evidence from the hypothesis test to mean that you...

    https://astarmathsandphysics.com/a-level-maths-notes/s2/3774-type-i-and-type-errors-the-power-of-a-test.html
  • Biased Estimators

    An estimator fora statistical parameter issaid to be biased if Bias is often impossible toavoid in practice and must be taken into account when statisicalcalculations are performed. Example: To estimate thenumber, ofnesting birds, scientists catch 100,...

    https://astarmathsandphysics.com/a-level-maths-notes/s3/3777-biased-estimators.html
  • Estimating Population Mean and Variance From a Sample

    In practice most of statisitics involves taking and analysing samples. The most important statistical measures for any sample are the mean and variance (or the standard deviation ). We usually do not know the mean and standard deviation of the...

    https://astarmathsandphysics.com/a-level-maths-notes/s3/3782-estimating-population-mean-and-variance-from-a-sample.html
  • Unbiased Estimators

    An estimator fora statistical parameter issaid to be unbiased if The mean of a sample isan unbiased estimator of the population mean Thiscan be used in a less obvious way in the following example. A bag has 500 beans of twocolours, black and white. A...

    https://astarmathsandphysics.com/a-level-maths-notes/s3/3796-unbiased-estimators.html
  • The Mann Whitney U Test

    The Mann Whitney U test allows the comparison of two independent random samples (1 and 2). The Mann Whitney U statistic is defined as: - where samples of size and are pooled and R i are the ranks of sample 1. U can be resolved as the number of times...

    https://astarmathsandphysics.com/a-level-maths-notes/s6/3821-the-mann-whitney-u-test.html
  • The Standardised Score

    The standardized score is a statistical tool that allows comparison of related quantities that are normally distributed. A very good use is test scores. When a student wishes to compare their own results with everybody elses, they may stanaridize their...

    https://astarmathsandphysics.com/a-level-maths-notes/s1/3742-the-standardised-score.html
  • The Two Sample Paired t -test

    The paired t test is typically used to analyse whether there is a before and after difference. It is the same population before and after, and the difference for each individual is measured and a mean difference found and analysed for significance. For...

    https://astarmathsandphysics.com/a-level-maths-notes/s4/3818-the-two-sample-paired-t-test.html
  • A* Maths/Physics Tuition Throughout London & Online Tests/Notes

    Tuition for every A Level and International A Level(CIE/Edexcel) module - Core C1/C2/C3/C4, Mechanics M1/M2/M3/M4/M5/M6, Statistics S1/S2/S3/S4/S5/S6, Further Pure FP1/FP2/FP3/FP4 and Decision D1/D2, and physics tuition for every AS and A2 module and...

    https://astarmathsandphysics.com/
  • University Maths and Physics Tuition

    Maths and Physics Topics Up To Degree Level: Fluid Dynamics Approximation Theory Topology Differential Geometry Calculus Statistics Electromagnetism Quantum Mechanics Non Linear Dynamics Mechanics Group Theory Optics Galois Theory Physical Chemistry...

    https://astarmathsandphysics.com/79-main/72-university-maths-and-physics-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
  • Private Physics Tuition by Specialist Tutors

    draw conclusions about whether or not the result of an experiment was significant or not without knowing something about statistics and error analysis. A lot of physics can be done with quite basic maths - just substituting numbers into the right...

    https://astarmathsandphysics.com/physics.html
  • Pie Charts

    60 children go to school. There are various methods they use – they may walk, go by car, bus or train. The statistics are in the following table. Method of Going to School Frequency Angle Walk 21 Car 15 Bus 20 Train 4 Total 60 360 Because it is for a...

    https://astarmathsandphysics.com/gcse-maths-notes/618-pie-charts.html
  • Sampling Methods

    Gathering statistics involves time and effort. It is a necessary procedure – governments need to know how many schools to build, or policemen to employ, and companies need to know which products people will buy. They could go out and ask everyone, but...

    https://astarmathsandphysics.com/gcse-maths-notes/645-sampling-methods.html
  • Counting Permutations

    Permutations is that part of statistics involving arrangements of objects, some of which fall in the same group and some of which fall in different groups. Each object is distinct from all the other objects, so we can tell each one apart, and if two...

    https://astarmathsandphysics.com/ib-maths-notes/counting-permutations-and-combinations/962-counting-permutations.html
  • Permutations

    Permutations is that part of statistics involving arrangements of objects, some of which fall in the same group and some of which fall in different groups. Each object is distinct from all the other objects, so we can tell each one apart, and if two...

    https://astarmathsandphysics.com/a-level-maths-notes/s1/3723-permutations.html
  • Hypothesis Testing, Critical Values and Critical Regions

    thesecould be written down on the side of a machine and used by someonewho knows nothing about hypothesis testing or statistics. If the nullhypothesis is rejected, the machine could be stopped and checked foralignment for example.. Suppose we are...

    https://astarmathsandphysics.com/a-level-maths-notes/s2/3755-hypothesis-testing-critical-values-and-critical-regions.html

Results 121 - 140 of 148