Business Maths and Statistics 6e

Andre Francis, Queens Medical Centre, University of Nottingham
ISBN-13: 9781844801282
ISBN: 1844801284

[Purchase this ebook]

The sixth edition provides a thorough grounding in basic mathematical and statisical techniques for business students, and students on a professional course such as accounting. The result is a comprehensive, user-friendly, testing oriented guide to quantitative methods for business.

Chapter Abstracts

• Ch. 1. Introduction to Business Mathematics and Statistics  [Purchase this echapter]
  Chapter One covers the main areas covered under the heading of business mathematics and statistics: differences in terminology; business mathematics and statistics; statistical method; management mathematics, probability, statistical investigations; and stages in an investigation.
• Ch. 2. Sampling and data collection  [Purchase this echapter]
  Chapter Two covers sampling and data collection: primary and secondary data; censuses; samples; bias; sampling frames; sampling techniques; random sampling numbers; simple random sampling; stratification of a population; stratified sampling; systematic sampling; multi-stage sampling; cluster sampling; quota sampling; precision; sample size; methods of primary data collection; questionnaire design; the use of secondary data; sources of secondary data and their use; and official secondary data sources.
• Ch. 3. Data and their accuracy  [Purchase this echapter]
  Chapter Three covers data and their accuracy: data classification; discrete data; continuous data; rounding and its conventions; errors and their causes; maximum errors; methods of describing errors; rounding errors; errors in expressions; error rules; fair and biased rounding; compensating and systematic errors; and avoiding errors when using percentages.
• Ch. 4. Frequency distribution and charts  [Purchase this echapter]
  Chapter Four covers frequency distributions and charts: raw statistical data; data arrays; simple frequency distributions; grouped frequency distributions; definitions associated with frequency distribution classes; rules and practices for compiling grouped frequency distributions; formation of grouped frequency distributions; histograms; frequency polygons and curves; cumulative frequency distributions; cumulative frequency polygons and curves; Lorenz curves; and interpretation and characteristics of Lorenz curves.
• Ch. 5. General charts and graphs  [Purchase this echapter]
  Chapter Five covers general charts and graphs: non-numeric frequency distributions; time series; purpose of statistical diagrams; types of charts and graphs; pictograms; some features of pictograms; simple bar charts; some features of simple bar charts; pie charts; some features of pie charts; line diagrams; some features of line diagrams; component, percentage and multiple bar charts; comparison of component, percentage and multiple bar charts; multiple pie charts; proportional pie charts; strata charts; Z-charts; Gantt charts; actual and percentage increases in time series; semi-logarithmic graphs; and checklist for the construction of diagrams.
• Ch. 6. Arithmetic mean  [Purchase this echapter]
  Chapter Six covers the arithmetic mean: the definition of the arithmetic mean; notation for general values; notation for the sum of values; formula for the mean of a set of values; the mean of a simple frequency distribution; the mean of a grouped frequency distribution; formula for the mean of a frequency distribution; manipulation of the mean formula; weighted means; and significance of the mean.
• Ch. 7. Median  [Purchase this echapter]
  Chapter Seven covers the median: definition of the median; median for a simple frequency distribution; procedure for calculating the median; median for a grouped frequency distribution; estimating the median by formula; procedure for estimating the median by formula; estimating the median graphically; procedure for estimating the median graphically; comparison of formula and graphical techniques; median for a simple (continuous) frequency distribution; and characteristics of the median.
• Ch. 8. Mode and other measures of location  [Purchase this echapter]
  Chapter Eight covers mode and other measures of location: the mode; the mode for grouped data; mode of a grouped frequency distribution by formula; graphical estimation of the mode; characteristics of the mode; graphical comparisons of mean, median and mode; relationships between mean, median and mode; proportional increases and multipliers; formula for the geometric mean; note on calculation of the geometric mean; the harmonic mean; use of harmonic mean compared with arithmetic mean; characteristics of the geometric and harmonic means.
• Ch. 9. Measures of dispersion and skewness  [Purchase this echapter]
  Chapter Nine covers measures of dispersion and skewness: comparison of location, dispersion and skewness; measures of dispersion; the range; characteristics of the range; the mean deviation; formulae for the calculation of the mean deviation; characteristics of the mean deviation; other measures of dispersion; and skewness.
• Ch. 10. Standard deviation  [Purchase this echapter]
  Chapter Ten covers standard deviation: calculating the standard deviation; the link between the standard deviation and the mean; adaptation of the standard deviation formula; computational formula for the standard deviation of a set of values; standard deviation for a frequency distribution; formula for the standard deviation of a frequency distribution; characteristics of the standard deviation; the coefficient of variation; Pearson's measure of skewness; and the derivation of the standard deviation.
• Ch. 11. Quantiles and the quartile deviation  [Purchase this echapter]
  Chapter Eleven covers quantiles and the quartile deviation: quantiles and their use; quartiles; identification of the quartiles for a set; the quartile deviation; the place of the quartile deviation; identifying the quartiles of a frequency distribution; graphical estimation of quartiles; general interpolation formula for quantiles; the quartile coefficient of dispersion; quartile measure of skewness; and some other quantiles.
• Ch. 12. Linear functions and graphs  [Purchase this echapter]
  Chapter Twelve covers linear functions and graphs: linear functions and graphs; plotting a straight line; the gradient and y-intercept; determining the value of the gradient; and determining the equation of a given line.
• Ch. 13. Regression techniques  [Purchase this echapter]
  Chapter Thirteen covers regression techniques: regression and its uses; standard methods of obtaining a regression line; the 'y on x' regression line; the method of semi-averages; the background and basis of least squares regression; formula for obtaining the y on x least squares regression line; dependent and independent values; non-causal relationships; the least squares line and the mean point; interpolation and extrapolation; and diagrammatic illustration of interpolation and extrapolation.
• Ch. 14. Correlation techniques  [Purchase this echapter]
  Chapter Fourteen covers correlation techniques: the purpose of correlation; the definition and meaning of correlation; the correlation coefficient; the product moment correlation coefficient; positive correlation; negative correlation; diagrammatic demonstration of correlation; correlation, regression and variation; correlation, regression and variation; the coefficient of determination; Spearman's rank correlation coefficient; rank correlation and its uses; comparison of rank and product moment correlation; and correlation and causality.
• Ch. 15. Time series model  [Purchase this echapter]
  Chapter Fifteen covers the time series model: definition of a time series; time series cycle; time series models; time series analysis; standard time series models; description of time series components; and graphing a time series.
• Ch. 16. Time series trend  [Purchase this echapter]
  Chapter Sixteen covers time series trend: the significance of trend values; techniques for extracting the trend; the method of semi-averages; working data; the method of least squares regression; the method of moving averages; moving average centering; and comparison of techniques for trend.
• Ch. 17. Seasonal variation and forecasting  [Purchase this echapter]
  Chapter Seventeen covers seasonal variation and forecasting: the nature of seasonal variation; technique for calculating seasonal variation; seasonally adjusted time series; forecasting; technique for forecasting; projecting the trend; and forecasting and residual variation.
• Ch. 18. Index relatives  [Purchase this echapter]
  Chapter Eighteen covers index relatives: definition of an index number; simple index number construction; some notation; Index relatives; time series of relatives; changing the base of fixed-base relatives; comparing sets of fixed base relatives; actual and real values of a commodity; and time series deflation.
• Ch. 19. Composite index numbers  [Purchase this echapter]
  Chapter Nineteen covers composite index numbers: composite index numbers; weighting of components; types of composite index number; example data for calculating indices; weighted average of relatives; weighted aggregates; comparison of the two composite indices; Laspeyres indices; Paasche indices; comparison of Laspeyres and Paasche price indices; some considerations in the construction of index numbers; some uses of index numbers; and some limitations of index numbers.
• Ch. 20. Special published indices  [Purchase this echapter]
  Chapter Twenty covers special published indices: The Retail Prices Index; main RPI groups and their weights; The Family Expenditure Survey; price collection and calculation of the RPI; the Purchasing Power of the Pound (index); The Tax and Price Index; Producer Price Indices (PPI); Indices of Average Earnings; Index of Output of the Production Industries; Index of Retail Sales; and other index numbers.
• Ch. 21. Interest and depreciation  [Purchase this echapter]
  Chapter Twenty One covers interest and depreciation: progressions and interest; arithmetic progressions; geometric progressions; some terms used in business calculations; difference between simple and compound interest; formula for amount accrued (simple interest); formula for amount accrued (compound interest); notes on previous formula; notes on calculations involving compound interest; nominal and effective interest rates; formula for calculating APR; depreciation; straight line depreciation; reducing balance depreciation; and formula for reducing balance depreciation.
• Ch. 22. Present value and investment appraisal  [Purchase this echapter]
  Chapter Twenty Two covers present value and investment appraisal: present value; formula for present value; use of discounting tables; present value of an interest-bearing debt; capital investments; discounted cash flow; interpretation of NPV; internal rate of return (IRR); graphical estimation of IRR; estimation of IRR by formula; comparison of projects; and comparison of appraisal techniques.
• Ch. 23. Annuities  [Purchase this echapter]
  Chapter Twenty Three covers annuities: annuities and their uses; definition and types of annuity; some aspects and examples of annuities; notes on calculations involving annuities; accrued value of an invested annuity; net present value of an annuity; amortization annuity; amortization schedule; sinking funds; debt repayment using a sinking fund; sinking fund schedule; and sinking fund method of depreciation.
• Ch. 24. Functions and graphs  [Purchase this echapter]
  Chapter Twenty Four covers functions and graphs: functions and equations; linear and quadratic equations; special form of a linear function; quadratic functions and their graphs; cubic functions and equations; polynomials and turning points; and ratio of two linear functions.
• Ch. 25. Linear equations  [Purchase this echapter]
  Chapter Twenty Five covers linear equations: types of linear equations; general methods of solution; solving linear equations algebraically; solving linear equations graphically; the existence of solutions of equations; manipulating linear equations; procedure for solving 2x2 simultaneous equations; procedure for solving 2×2 simultaneous equations graphically; and procedure for solving 3×3 simultaneous equations algebraically.
• Ch. 26. Quadratic and cubic equations  [Purchase this echapter]
  Chapter Twenty Six covers quadratic and cubic equations: quadratic equations; techniques for solving quadratic equations; solving quadratic equations by formula; solving quadratic equations by factorization; solving quadratic equations graphically; graphs and the solution of equations; cubic equations; and graphical solution of cubic equations.
• Ch. 27. Differentiation and integration  [Purchase this echapter]
  Chapter Twenty Seven covers differentiation and integration: differentiation and integration and their use; simple functions; rule and notation for differentiation; an extension of differentiation; the practical interpretation of differentiation; second derivative of a function; the practical use of differentiation; procedure for identifying the turning points of a curve; integration; and notation and rule for integration.
• Ch. 28. Cost, revenue and profit functions  [Purchase this echapter]
  Chapter Twenty Eight covers cost, revenue and profit functions: the basic profit equation; the profit function; cost and revenue functions; cost functions; revenue functions; demand (price) function; identifying the demand function; and marginal cost and revenue functions.
• Ch. 29. Set theory and enumeration  [Purchase this echapter]
  Chapter Twenty Nine covers set theory and enumeration: sets and elements; further set concepts; Venn diagrams; operations on sets; set union; set intersection; set enumeration; an enumeration problem; solving an enumeration problem; defining the general enumeration problem; notation for the 2-set problemolution of the general enumeration problem; notation for the 3-set problem.
• Ch. 30. Introduction to probability  [Purchase this echapter]
  Chapter Thirty covers introduction to probability: the concept of probability; statistical experiments; outcomes of experiments; statistical events; definition of mutually exclusive events; definition of independent events; theoretical and empirical probability; definition of theoretical probability; definition of empirical probability; comparison of theoretical and empirical probability; further rules of probability; the addition rule for probabilities; the multiplication rule for probabilities; compound experiments and events; and tree diagrams.
• Ch. 31. Conditional probability and expectation  [Purchase this echapter]
  Chapter Thirty One covers conditional probability and expectation: expectation; formula for expected value (expectation); conditional probability; definition of conditional probability; the general multiplication rule for probability; probabilities involving split events; Bayes Theorem; and tabular solution of conditional probability problems.
• Ch. 32. Combinations and permutations  [Purchase this echapter]
  Chapter Thirty Two covers combinations and permutations: combinations and permutations; factorials; the combination formula; and the permutation formula.
• Ch. 33. Binomial and Poisson distributions  [Purchase this echapter]
  Chapter Thirty Three covers binomial and poisson distributions: a binomial distribution; binomial probability formula; use of the binomial probability formula; mean and variance of the binomial distribution; a poisson distribution; poisson probability formula; use of the poisson probability formula; notes on the poisson distribution; and poisson approximation to the binomial.
• Ch. 34. Normal distribution  [Purchase this echapter]
  Chapter Thirty Four covers normal distribution: the Normal distribution; Normal distribution probabilities; Z-scores; standard Normal (Z) tables; extending the use of tables; summary of procedure for calculating Normal probabilities; Normal approximation to the binomial; confidence limits; confidence limits for a mean; confidence limits for a proportion; and test of significance for the mean.
• Ch. 35. Linear inequalities  [Purchase this echapter]
  Chapter Thirty Five covers linear inequalities: the need for inequalities; linear inequalities; feasible regions; the linear programming problem; graphical solution to the linear programming problem; and practical notes on linear programming.
• Ch. 36. Matrices  [Purchase this echapter]
  Chapter Thirty Six covers matrices: a matrix structure; identifying data within a matrix; definition and description of a matrix; addition and subtraction of matrices; definition of matrix addition and subtraction; multiplying a matrix by a number; multiplying matrices together; factors involved in matrix multiplication; pictorial demonstration of matrix multiplication; the matrix multiplication size diagram; condition and procedure for matrix multiplication; additional features of matrices; solving simultaneous equations; solving 2 by 2 simultaneous equations using matrices; transition matrices; and definition of a transition matrix.
• Ch. 37. Inventory control  [Purchase this echapter]
  Chapter Thirty Seven covers inventory control: the need for an inventory; costs associated with inventories; inventory control purpose; some terminology; the inventory graph; some further terminology; inventory control systems; re-order level system; periodic review system; inventory models; the basic model; cost equation for basic model; definitions and formulae for basic model; adapted model (with gradual replenishment); definitions and formulae for adapted basic model; and derivation 1 - EOQ formula.
• Ch. 38. Network planning and analysis  [Purchase this echapter]
  Chapter Thirty Eight covers network planning and analysis: network planning; activities and events; dummy activities; summary of network planning procedures; critical path 1; earliest and latest event times; critical path 2; float; and tabular presentation of a network.