$55.50
A Concise Course in Advanced Level Statistics with worked examples Export Edition
US$ 55.50
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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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