EC255 Study Guide - Fall 2018, Comprehensive Midterm Notes - Statistical Inference, Sample Space, Histogram
EC255
MIDTERM EXAM
STUDY GUIDE
Fall 2018
Introduction to Statistics
What is Statistics?
• Statistics is the art and science of gathering, analyzing, interpreting, and presenting data
• Key issues:
o How to quantify data
o Transform data into information
o Transform information into knowledge
o How to deal with uncertainty
Vocabulary
• Measurement: process of transforming something our senses cannot perceive into something
they can receive
• Data: measurements that are collected, recorded, and summarized for presentation, analysis, and
interpretation
• Element: an entity or object on which data are collected (also called case, subject, individual)
• Variable: characteristic of the elements whose values may differ from element to element and is
of interest to the data collector
• Observation: measurement of a variable or variables on a single element
• Types of data:
o Qualitative: labels or names for a characteristic
o Quantitative: measurement of amount or quantity (discrete or continuous)
• Data management: categorization of the values of a variable according to the amount of
information conveyed about the elements to which they correspond
• Nominal level: values represent category or group membership of elements (is A=B? i.e. eye
colour)
find more resources at oneclass.com
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• Ordinal level: values convey less than, equal to, and greater than relationships among elements
(i.e. relative ranks of elements with respect to their values for the variable in question, A>B or
A<B)
• Interval level: values convey how much more or less one value is than another value (how much is
A-B? i.e. temperature)
• Ratio level: values can take on a natural or absolute zero (how much is A/B?)
Data Measurement Examples
• Discrete ratio
o How many automobiles do you currently own? __ (number) (from zero)
• Continuous interval
o What is the high temperature today? __ (Celsius) (can go below zero, could take on decimal
value)
• Continuous ratio
o What is your animal income? __ ($) (can have decimals)
• Nominal
o Are you married? (yes or no)
• Ordinal
o How would you rate the value of the product (excellent, good, fair, poor)
More Vocabulary
• Population
o Collection of ALL possible elements of interest (i.e. everyone in Canada who voted in the last
election)
• Census
o Collection of values for all variables (i.e. did you vote in the last election?) of interest that
correspond to all elements of a population
o Size usually denoted by "N"
• Parameter
o Descriptive measure of a population (i.e. age of people who voted)
• Sample
o Collection of elements drawn from the population (i.e. subset of the population)
• i.e. sample of 365 voters from last election
o Size usually denoted by "n"
find more resources at oneclass.com
find more resources at oneclass.com
Document Summary
Statistics is the art and science of gathering, analyzing, interpreting, and presenting data: key issues, how to quantify data, transform data into information, transform information into knowledge, how to deal with uncertainty. Interval level: values convey how much more or less one value is than another value (how much is. A-b? i. e. temperature: ratio level: values can take on a natural or absolute zero (how much is a/b?) __ ($) (can have decimals: nominal, are you married? (yes or no, ordinal, how would you rate the value of the product (excellent, good, fair, poor) Sample: collection of elements drawn from the population (i. e. subset of the population, collection of elements drawn from the population (i. e. subset of the population) i. e. sample of 365 voters from last election, size usually denoted by n Statistic: an estimate of the value of a parameter based on the elements that belong to the sample (i. e. average age of voters was 32)
