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Join The Student Room TodayBe part of the UK's largest and fastest growing student community. It's free to join and a lot of fun - Get inspired, express your ideas, interact and share A Level Mathematics S1 Revision NotesFrom The Student RoomTSR Wiki > Study Help > Subjects and Revision > Revision Notes > Mathematics > A Level Mathematics S1 Revision Notes
Representing Data(a) For the class 5 – 9 Lower class boundary is 4.5 Upper class boundary is 9.5 Class boundary = 5 Class midpoint: (b) Histogram: Frequency density = Histograms are plotted by Frequency density against Class boundary ProbabilityThe probability, p, of something is the likelihood of that event occurring. The sample space is every single possible outcome, while an event is a set of possible outcomes. A Venn diagram shows the sample space, and a Tree diagram shows the events.
If 2 events are independent, then If 2 events are mutually exclusive, then Discrete Random VariablesDiscrete Random Variables are ones which can only take certain values, and not the values in between. A probability function describes the probability of each outcome, and a probability distribution is a table of all the outcomes along with their probabilities. A cumulative distribution function is in the form F(x), and is the probability of all the values of outcomes up to and including x. The sum of all probabilities must equal 1.
Discrete Uniform DistributionNot necessary, but saves time in an exam. A discrete uniform distribution is when all outcomes have an equal probability of occurring (e.g. a die roll). For a discrete uniform distribution:
Continuous Random VariablesThe Normal DistributionThe probability distribution of a continuous random variable is represented by a curve; the area under the curve in a given interval gives the probability of a value lying in that interval. If X is normally distributed with mean µ and standard deviation σ, then X~N(µ,σ^2) If Z is a continuous random variable, where Z~N(0,1) then Φ(z) = P(Z<z) The variable Z=(X-μ)/σ is the standard normal variable corresponding to X. The percentage points table shows, for a probability p, the value of z such that P(Z<z) = p Correlation2 variables are positively correlated if one increases with the other, and negatively correlated if one decreases as the other increases. The variables are usually plotted on a scatter diagram. Correlation is measured by the Product Moment Correlation Coefficient (PMCC), r, where:
where:
It is also possible to code the x and y values. If RegressionThe independent/explanatory variable, usually x, is the one which can be set, while the dependent/response variable, y is the one which depends on the values of x. Linear regression can be calculated by the least squares regression line
Interpolation is using the regression line to estimate y given x, while extrapolation is using the line to estimate y with a value of x outside the range of values used for the line. Extrapolation is not very useful as you do not know if the trend continues outside your range of values. Estimating and Samples |
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