A complete and in-depth summary of Chapters 1-4 of the prescribed coursework for STAT1000. Although a mathematical course is one which usually requires merely application, Business Statistics contains a lot of information which must be learnt. I have found these colourful summaries to be very usefu...
BUSINESS STATISTICS I
STAT 1000
CHAPTER 1 - 4 SUMMARIES
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,CHAPTER 1: DESCRIPTIVE STATISTICS
Introduction
• Statistics: word commonly used to describe numerical information
a field of study that deals with the collection, analysis, interpretation and presentation of numerical data
• Study of statistics divided into two areas:
- Descriptive statistics: deals with results obtained from collecting data on a group of people/items and reaching
valid conclusions only on that group (sample)
- Inferential statistics: deals with results obtained from collecting data on a subset of people/items (sample) and
reaching conclusions about a full set of people/items (population), from which the sample was selected
Chapter Formulae
Terminology
• Population: a complete or exhaustive collection of people, objects or items to be studied. The total number of items in a
population is referred to as the population size and is denoted with a capital letter N
• Sample: subset or portion of the population from which data are collected. The sample size is denoted with a lowercase
letter n (Sample = Statistic)
• Data: entire collection of information gathered from a sample
• Variable: property or characteristic of the items of the population that we would like to measure or record which are
denoted by capital letters and their values denoted by lowercase letters
• Categorical variables: variables that have two or more categories
- Nominal variables: categorical variables where the categories have no implicit ordering, such
gender
- Ordinal variables: categorical variables that consist of categories which can be arranged in a
logical order
, • Numerical variables: variables that yield numerical responses
- Discrete: numerical variable that can take on whole numbers only
- Continuous: numerical variable that can take on any value in an interval
• Parameter: descriptive summary measure calculated from population data (Parameter = Population)
use sample information to estimate population parameters, which forms part of inferential statistics
• Statistic: descriptive summary measure calculated from sample data
Data Types
• Raw/ungrouped data
- first data collected
- record all information (variables) for all individuals (observations)
• Grouped data
- use raw data to construct a table where the frequency distribution of a variable is summarised
- format depends on nature of variable
- Grouped discrete data: frequency table of a discrete variable
- Grouped continuous data: frequency table of a continuous variable or a discrete variable grouped into intervals
Grouped discrete data
• Grouped discrete table lists all possible values of a discrete variable followed by the number of times each value
occurs in the sample
• First order the data in ascending order to form an ordered array
• Count of how many times a value occurs = frequency of occurrence which tells how often/frequently an observed
value occurs within the data
• Collection of all frequencies describes how the data is distributed across the variable therefore termed frequency
distribution
Grouped continuous data
• If there is a large range of discrete values or continuous data, frequency table will not adequately show the distribution
of the variable
• First group the data into intervals (classes) then count the number of observations that fall into each class (frequency)
• Creating class intervals requirements:
- convenient
- keep classes equal in length to clearly indicate distribution
- first class must start below smallest value
- last class must end above largest value
- each class must consist of a lower limit and an upper limit
- classes MUST NOT overlap
Relation between Raw and Ungrouped Data
• All variables start as raw data and can be tabulated into either grouped discrete or grouped continuous data
• In grouped discrete data the original raw data are represented without loss of information therefore possible to
recreate the raw data from grouped discrete data
• In grouped continuous data, grouping the data into classes leads to a loss of information as we no longer represent
the individual observed information therefore we cannot recreate the original data from the tabulated data
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