A Concise Course in Advanced Level Statistics with worked examples Export Edition
$50.25

A Concise Course in Advanced Level Statistics with worked examples Export Edition

By Joan Sybil Chambers, D J Crawshaw, Brian Jefferson, David Bowles, Eddie Mullan, Garry Wiseman, John Rayneau, Mike Heylings, Rob Wagner, Steve Cavill, Tony Beadsworth, C P Rourke, Mark Gaulter, Brian Gaulter, Robert Smedley, Ian Cook, Graham Upton, Thorning, Sadler
US$ 50.25
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Book Description

This best-selling book remains the most popular stand-alone text for Advanced Level Statistics. It covers the AS and A2 specifications in Statistics for Advanced Level Maths across all boards.

Table of Contents
  • Front Cover
  • IFC
  • Imprint
  • Contents
  • Preface
  • 1 Representation and summary of data
    • Discrete data
    • Continuous data
    • Stem and leaf diagrams (stemplots)
    • Ways of grouping data
    • Histograms
    • Frequency polygons
    • Frequency curves
    • Circular diagrams or pie charts
    • The mean
    • Variability of data
    • The standard deviation, s, and the variance, s²
    • Combining sets of data
    • Scaling sets of data
    • Using a method of coding to find the mean and standard deviation
    • Cumulative frequency
    • Cumulative percentage frequency diagrams
    • Median, quartiles and percentiles
    • Skewness
    • The normal distribution
    • Box and whisker diagrams (box plots)
    • Summary
  • 2 Regression and correlation
    • Scatter diagrams
    • Regression function
    • Linear correlation and regression lines
    • The product-moment correlation coefficient, r
    • Spearman’s coefficient of rank correlation, r
    • Summary
  • 3 Probability
    • Experimental probability
    • Probability when outcomes are equally likely
    • Subjective probabilities
    • Probability notation and probability laws
    • Illustrating two or more events using Venn diagrams
    • Probability rule for combined events
    • Exclusive (or mutually exclusive) events
    • Exhaustive events
    • Conditional probability
    • Independent events
    • Probability trees
    • Bayes’ Theorem
    • Some useful methods
    • Arrangements
    • Permutations of r objects from n objects
    • Combinations of r objects from n objects
    • Summary
  • 4 Probability distributions I – discrete variables
    • Probability distributions
    • Expectation of X, E(X)
    • Expectation of any function of X, E(g(X))
    • Variance, Var(X) or V(X)
    • The Cumulative distribution function, F(x)
    • Two independent random variables
    • Distribution of X₁ + X₂ +⋯+ X
    • Comparing the distributions of X₁ + X₂ and 2X
    • Summary
  • 5 Special discrete probability distributions
    • The uniform distribution
    • The geometric distribution
    • Expectation and variance of the geometric distribution
    • The binomial distribution
    • Expectation and variance of the binomial distribution
    • The Poisson distribution
    • Using the Poisson distribution as an approximation to the binomial distribution
    • The sum of independent Poisson variables
    • Summary
  • 6 Probability distributions II – continuous variables
    • Continuous random variables
    • Probability density function (p.d.f.)
    • Expectation of X, E(X)
    • Expectation of any function of X
    • Variance of X, Var(X)
    • The mode
    • Cumulative distribution function F(x)
    • Obtaining the p.d.f., f(x), from the cumulative distribution function
    • The continous uniform (or rectangular) distribution
    • Expectation and variance of the uniform distribution
    • The cumulative distribution function, F(x), for a uniform distribution
    • Summary
  • 7 The normal distribution
    • Finding probabilities
    • The standard normal variable, Z
    • Using standard normal tables
    • Using standard normal tables for any normal variable, X
    • Using the standard normal tables in reverse to find z when Φ(z) is known
    • Using the tables in reverse for any normal variable, X
    • Value of μ or σ or both
    • The normal approximation to the binomial distribution
    • Continuity corrections
    • Deciding when to use a normal approximation and when to use a Poisson approximation for a binomial distribution
    • The normal approximation to the Poisson distribution
    • Summary
  • 8 Linear combinations of normal variables
    • The sum of independent normal variables
    • The difference of independent normal variables
    • Multiples of independent normal variables
    • Summary
  • 9 Sampling and estimation
    • Sampling
    • Surveys
    • Sampling methods
    • Simulating random samples from given distributions
    • Sample statistics
    • The distribution of the sample mean
    • Central limit theorem
    • The distribution of the sample proportion, p
    • Unbiased estimates of population parameters
    • Point estimates
    • Interval estimates
    • The t-distribution
    • Confidence intervals for the population proportion, p
    • Summary
  • 10 Hypothesis tests: discrete distributions
    • Hypothesis test for a binomial proportion, p (small sample size)
    • Procedure for carrying out a hypothesis test
    • One-tailed and two-tailed tests
    • Summary of stages of a hypothesis (significance) test
    • Type I and Type II errors
    • Significance test for a Poisson mean λ
    • Summary of stages of a significance test
    • Summary of Type I and Type II errors
  • 11 Hypothesis testing (z-tests and t-tests)
    • Hypothesis testing
    • One-tailed and two-tailed tests
    • Critical z-values
    • Summary of critical values and rejection criteria
    • Stages in the hypothesis test
    • Hypothesis test 1: testing μ (the mean of a population)
    • Type I and Type II errors
    • Hypothesis test 2: testing a binomial proportion p when n is large
    • Hypothesis test 3: testing μ₁ − μ₂, the difference between means of two normal populations
    • Summary
  • 12 The χ² significance test
    • The χ² significance test
    • Performing a χ² goodness-of-fit test
    • Summary of the procedure for performing a χ² goodness-of-fit test
    • Test 1 – goodness-of-fit test for a uniform distribution
    • Test 2 – goodness-of-fit test for a distribution in a given ratio
    • Test 3 – goodness-of-fit test for a binomial distribution
    • Test 4 – goodness-of-fit test for a Poisson distribution
    • Test 5 – goodness-of-fit test for a normal distribution
    • Summary of the number of degrees of freedom for a goodness-of-fit test
    • The χ² significance test for independence
    • Summary
  • 13 Significance tests for correlation coefficients
    • Significance tests for correlation coefficients
    • Test for the product-moment correlation coefficient, r
    • Spearman’s coefficient of rank correlation, r
    • Summary
  • ICT statistics supplement
  • Appendix
    • Cumulative binomial probabilities
    • Cumulative Poisson probabilities
    • The standard normal distribution function
    • Critical values for the normal distribution
    • Critical values for the t-distribution
    • Critical values for the χ² distribution
    • Critical values for correlation coefficients
    • Random numbers
  • Answers
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