Business Statistics

Business Statistics Chapter 1 – Introduction and Data Collection Basic Concepts Variables are characteristics of items or individuals. Data are the observed values of variables. A population is a collection of all members of a group being investigated. A sample is a portion of the population selected for analysis.

A parameter is a numerical measure describing a characteristic of a population. A statistic is a numerical measure describing a characteristic of a sample. Statistics is divided into 2 branches: – –

Descriptive Statistics: Collecting, summarising and presenting a set of data Inferential Statistics: Uses sample data to draw conclusions about a population

Types of Variables The two types of variables are: –

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Categorical (Qualitative)  Nominal (non-ordered labels e.g. Yes/No)  Ordinal (ordered labels e.g. Satisfied/Neutral/Unsatisfied) Numerical (Quantitative)  Discrete  Continuous

Levels of Measurement Scales

Chapter 2 – Presenting Data in Tables and Charts Tables and Charts for Categorical Data Summary Tables give the frequency, proportion and percentage of data values in each category. –

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Bar Charts  Preferred for comparing frequencies and proportion (0.28) or percentages (28%) of categories Pie Charts  Preferred for observing the portion of the total which lies in a particular category

Organising Numerical Data – –

Ordered Arrays  Numerical data sorted by order of magnitude Stem-and-Leaf Displays  Graphical representation of numerical data

Tables and Charts for Numerical Data Numerical Summary Measures  mean, median, standard deviation and variance –

Distribution Tables  Frequency: data are arranged into ordered intervals  To determine Interval Width: range/no. of intervals *no more than 10 intervals  Relative Frequency: obtained by dividing the frequency in each interval by the total number of values  Percentage: obtained by multiplying each relative frequency by 100  Cumulative Percentage: percentage of values that are less than a certain number

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Histograms  Graphical representation of a distribution table Percentage Polygon and Cumulative Percentage Polygons (Ogives)  Graphical representation of a percentage distribution

Scatter Diagrams and Time-Series Plots –

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Scatter Diagrams  Used to examine the relationship between two numerical variables *Independent Variable = x axis Dependent Variable = y axis Time-Series Plots  Used to examine patterns in the values of a variable over time

Chapter 3 – Numerical Descriptive Measures Measures of Central Tendency, Variation and Shape Central Tendency –

Mean

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Affected by outliers

Median

  –

Midpoint of ordered values

Mode

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Most frequently observed value

Quartiles

– Q1: – Q3: Variation (spread of data values) – – –

Range  Largest Value – Smallest Value Inter-Quartile Range  Q3 – Q1 Variance 

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Standard Deviation 

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Coefficient of Variation 

Shape Distributions

Chapter 4 – Basic Probability Basic Concepts Probability is a numerical measure of the likelihood that a particular event will occur. The Sample Space of a random experiment is the list of all possible outcomes of the experiment. E.g. Roll of a die: S = {1, 2, 3, 4, 5, 6} An Event is a collection of outcomes E.g. Event A of “an even number on a die”: The Complement (

) of Event A consists of all outcomes except in A.

Intersection and Union

Joint Probability –

Occurrence of two or more characteristics E.g. P(A∩B)

Marginal Probability –

Occurrence of a simple event E.g. P(A)

There are 3 ways of assigning probabilities: –

Classical Approach  Outcomes of an experiment are equally likely E.g. tossing a coin

A = {2, 4, 6}

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Relative Frequency Approach  Based on how often the outcome occurred previously Subjective Approach  Based on an individual’s belief that the event occurs

Conditional Probability P(A|B): probability of A occurring, given that B has occurred

Multiplication Rule Obtained by re-arranging the Conditional Probability Rule

Independent Events A and B are Independent Events if: – – –

P(A|B) = P(A) P(B|A) = P(B) P(A∩B) = P(A) x P(B)

The Addition Rule P(A U B) = P(A) + P(B) ─ P(A∩B) Mutually Exclusive Events If events A and B cannot occur simultaneously (at the same time), they are said to be mutually exclusive. P(A∩B) = 0 Therefore, the Addition Rule for these events: Probability Trees

P(A U B) = P(A) + P(B)