$58.49

# Introducing Statistics

By Ian Cook, Graham Upton, Thorning, Sadler

US$ 58.49

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Book Description

Introducing Statistics covers all the statistics required for single-subject Advanced Level Mathematics and also provides the basis for a first course in statistics in higher education. This is a highly accessible resource, supported by clear illustrations, nearly 200 worked examples, and packed with examination style questions.

Table of Contents

- Front Cover
- IFC
- Imprint
- Contents
- Preface to the Second Edition
- Preface to the First Edition
- Glossary of Notation
- 1 Summary diagrams and tables
- 1.1 The purpose of Statistics
- 1.2 Variables and observations
- 1.3 Types of data
- 1.4 Tally charts and frequency distributions
- 1.5 Stem-and-leaf diagrams
- 1.6 Bar charts
- 1.7 Multiple bar charts
- 1.8 Compound bars for proportions
- 1.9 Pie charts
- 1.10 Grouped frequency tables
- 1.11 Difficulties with grouped frequencies
- 1.12 Histograms
- 1.13 Frequency polygons
- 1.14 Cumulative frequency diagrams
- Step diagrams

- 1.15 Cumulative proportion diagrams
- 1.16 Time series
- 1.17 Scatter diagrams
- 1.18 Choosing which display to use
- 1.19 Dirty Data
- Chapter summary

- 2 Summary statistics
- 2.1 The purpose of summary statistics
- 2.2 The mode
- Modal class

- 2.3 The median
- 2.4 The mean
- 2.5 Advantages and disadvantages of the mode, mean and median
- Advantages
- Disadvantages

- 2.6 Sigma (Σ) notation
- Applications of sigma notation

- 2.7 The mean of a frequency distribution
- 2.8 The mean of grouped data
- 2.9 Using coded values to simplify calculations
- 2.10 The median of grouped data
- 2.11 Quartiles, deciles and percentiles
- Grouped data
- Ungrouped data

- 2.12 Range, inter-quartile range and midrange
- 2.13 Box-whisker diagrams
- Refined boxplots

- 2.14 Deviations from the mean
- 2.15 The variance
- Using the divisor n
- Using the divisor (n - 1)

- 2.16 Calculating the variance
- 2.17 The sample standard deviation
- Approximate properties of the standard deviation

- 2.18 Variance and standard deviation for frequency distributions
- 2.19 Variance calculations using coded values
- 2.20 Symmetric and skewed data
- 2.21 The weighted mean and index numbers
- Chapter summary

- 3 Data collection
- 3.1 Data collection by observation
- 3.2 The purpose of sampling
- 3.3 Methods for sampling a population
- The simple random sample
- Cluster sampling
- Stratified sampling
- Systematic sampling
- Quota sampling
- Self-selection
- A national survey

- 3.4 Random numbers
- Pseudo-random numbers
- Tables of random numbers

- 3.5 Methods of data collection by questionnaire (or survey)
- The face-to-face interview
- The postal questionnaire
- The telephone interview

- 3.6 Questionnaire design
- Some poor questions
- Some good questions
- The order of questions
- Question order and bias
- Filtered questions
- Open and closed questions
- The order of answers for closed questions
- The pilot study

- 3.7 Primary anf secondary data
- Chapter summary

- 4 Probability
- 4.1 Relative frequency
- 4.2 Preliminary definitions
- 4.3 The probability scale
- 4.4 Probability with equal likely outcomes
- 4.5 The complementary event, E
- 4.6 Venn diagrams
- 4.7 unions and intersections of events
- 4.8 Mutually exclusive events
- The additional rule

- 4.9 Exhaustive events
- 4.10 Probability trees
- 4.11 Sample proportions and and probability
- 4.12 Unequally likely possibilitie
- 4.13 Physical independence
- The multiplication rule

- 4.14 Orderings
- Orderings of similar objects

- 4.15 Permutations and combinations
- 4.16 Sampling with replacement
- 4.17 Sampling without replacement
- 4.18 Conditional probability
- The generalised multiplication rule

- 4.19 Statistical independence
- 4.20 The total probability theorem
- 4.21 Bayes theorem
- Chapter summary

- 5 Probability distrubutions and expectations
- 5.1 Notation
- 5.2 Probability distributions
- The probability function
- Illustrating probability disctributions
- Estimating probability distributions
- The cumulative distribution function

- 5.3 Some special discrete probability distributions
- The discrete uniform distribution
- The Bernoulli distribution

- 5.4 The geomatric distribution
- Notation
- Cumulative probabilities
- A paradox!

- 5.5 Expectations
- Expected value or expected number
- Expectation of X²

- 5.6 The variance
- 5.7 The standard deviation
- 5.8 Greek notation
- Chapter summary

- 6 Expectation algebra
- 6.1 E(X + a) and Var(X + a)
- 6.2 E(aX) and Var(aX)
- 6.3 E(aX + b) and Var(aX + b)
- 6.4 Expectations involving more than one variable
- Var(X + Y)
- E(X₁ + X₂) and Var (X₁ + X₂2)
- The difference between 2X and X₁ + X₂

- 6.5 The expectation and variance of the sample mean
- 6.6 The unbiased estimate of the population variance
- Chapter summary

- 7 The binomial distribution
- 7.1 Derivation
- 7.2 Notation
- 7.3 Successes and failures
- 7.4 The shape of the distribution
- 7.5 Tables of binomial distributions
- 7.6 The expectation and variance of a binomial random variable
- Chapter summary

- 8 The Poisson distribution
- 8.1 The Poisson process
- 8.2 The form of the distribution
- 8.3 The shape of a Poisson distribution
- 8.4 Tables for Poisson distributions
- 8.5 The Poisson approximation to the binomial
- 8.6 Sums of independant Poisson random variables
- Chapter summary

- 9 Continuous random variables
- 9.1 Histograms and sample size
- 9.2 The probability density function, f
- Properties of the pdf

- 9.3 The cumulative distribution function F
- The median, m

- 9.4 Expectation and variance
- 9.5 Obtaining f from F
- 9.6 Distribution of a function of a random variable
- 9.7 The uniform (rectangular) distributions
- Chapter summary

- 10 The normal distribution
- 10.1 The standard normal distribution
- 10.2 Tables of Φ (z)
- 10.3 Probabilities for other normal distributions
- 10.4 Finer detail in the tables of Φ (z)
- 10.5 Tables of percentage points
- 10.6 Using calculators
- 10.7 Applications of the normal distribution
- 10.8 General properties
- 10.9 Linear combinations of independant normal random variables
- Extension to more than two variables
- Distribution of the mean of normal random variables

- 10.10 The Central Limit Theorem
- The distribution of the sample mean, X
- 10.11 The normal approximation to a binomial distribution
- Inequalities
- Choosing between the normal and Poisson approximations to a binomial distribution

- 10.12 The normal approximation to a Poisson distribution
- Chapter summary

- 11 Point and internal estimation
- 11.1 Point estimates
- 11.2 Confidence intervals
- 11.3 Confidence interval for a population mean
- Normal distribution with known variance
- Unknown population distribution, known population variance, large sample
- Unknown population distribution, unknown population variance, large scale
- Poisson distribution, large mean

- 11.4 Confidence interval for a population proportion
- 11.5 The t-distribution
- Tables of the t-distribution

- 11.6 Confidence interval for a population mean using the t-distribution
- Chapter summary

- 12 Hypothesis tests
- 12.1 The null and alternative hypotheses
- 12.2 Critical regions and significance levels
- 12.3 The general test procedure
- 12.4 Test for mean, known variance, normal distribution or large sample
- 12.5 Identifying the two hypotheses
- The null hypothesis
- The alternative hypothesis

- 12.6 Test for mean, large sample, variance unknown
- 12.7 Test for large Poisson mean
- 12.8 Test for proportion, large sample
- 12.9 Test for mean, small sample, variance unknown
- 12.10 The p-value approach
- 12.11 Hypothesis tests and confidence internvals
- 12.12 Type I and Type II errors
- The general procedure

- 12.13 Hypothesis tests for a proportion based on a small sample
- 12.14 Hypothesis tests for a Poisson mean based on a small sample
- 12.15 Comparison of two means
- 12.16 Comparison of two means - known population variances
- Confidence interval for the common mean

- 12.17 Comparison of two means - common unknown population variance
- Large sample sizes
- Small sample sizes

- Chapter summary

- 13 Goodness of fit
- 13.1 The chi-squared distribution
- Properties of the chi-squared distribution
- Tables of the chi-squared distribution

- 13.2 Goodness of fit to prescribe probabilities
- 13.3 Small expected frequencies
- 13.4 Goodness of fit to prescribe distribution type
- 13.5 Contingency tables
- The Yates correction

- Chapter summary

- 13.1 The chi-squared distribution
- 14 Regression and correlation
- 14.1 The equation of a straight line
- Determining the equation

- 14.2 The estimated regression line
- 14.3 The method of least squares
- 14.4 Dependant random variable Y
- 14.5 Transformations, extrapolation and outliners
- 14.6 Confidence intervals and significance tests for the population regression coefficient β
- Mean and variance of the estimator of β
- Significance test for the regression coefficient

- 14.7 Confidence intervals and significance tests for the intercept x and for the expected value of Y, with known σ²
- 14.8 Distinguishing x and Y
- 14.9 Deducing x from a Y-value
- 14.10 Two regression lines
- 14.11 Correlation
- Nonsense correlation

- 14.12 The product-moment correlation coefficient
- The population product-moment correlation coefficient, p
- Testing the significance of r

- 14.13 Spearmans rank correlation coefficient
- Testing the significance
- Alternative table formats

- 14.14 Using r for non-linear relationships
- Chapter summary

- 14.1 The equation of a straight line
- Appendices
- Cumulative probabilities for the binomial distribution
- Cumulative probabilities for the Poisson distribution
- The normal distribution function
- Upper-tail percentage points for the standard normal distribution
- Percentage points for the t-distribution
- Percentage points for the x² distribution
- Critical values for the product-moment correlation coefficient
- Critical values for Spearmans rank correlation coefficient
- Random number

- Answers
- Index
- IBC
- Back Cover

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