Lectures 1 2 Week 1 Language Describing Data

Lectures 1 -2 Week 1 • Language Describing Data by Tables and Graphics • Chapter 1 (and 0) 1/10/2022 Language 1

Language • What is a variable? – Example • What is an Experimental Unit? – Example • What is a measurement (or data)? – Example • What are sampling, sample, populations? – Example 1/10/2022 Language 2

Why we need sampling • Example 1 record Body temperature for every healthy person on Earth!!! • Example 2 Legislative preference in Canada 1/10/2022 Language 3

Data • Univariate data – Example • Bivariate data – Example • Multivariate data – Example 1/10/2022 Language 4

Descriptive and Inferential Statistics • Descriptive (sample) – Example • Inferential Statistics (Population) – Example 1/10/2022 Language 5

Types of variables • Qualitative ( or Categorical) – Examples • Quantitative – Examples 1/10/2022 Language 6

Two types of quantitative data • Discrete: Finitely many or countable values – Examples • Continuous: over an interval – Examples 1/10/2022 Language 7

Describing Categorical data by tables and graphs Get the information: § § What values have been measured How often each value has occurred § Get tables or graphs as a summary 1/10/2022 Language 8

Graphical Tools • Frequency • Relative frequency • Percent • Rules: Sum up to n, 1, 100% respectively. 1/10/2022 Language 9

Example 1: Summarizing an Opinion Poll by a table • 280 undergrad students polled, their opinion about a proposed change in dormitory regulations. • Choices are 3: Support, Oppose, Neutral. • Results: 152, 51, 77 respectively. 1/10/2022 Language 10

Example 2 ( Using graphs) • 400 school administrators have been surveyed to rate the quality of public education in USA. They ranked it using A, B, C, or D. • Pie chart • Bar chart 1/10/2022 Language 11

Describing Quantitative Data • Example 1 The amount per category of money spent by US defense dept. in 2000 • That is the Variable X=“amount of money spent” is measured for several categories Draw a Pie chart for this data. 1/10/2022 Language 12

Quantitative (Cont’) • Example 2 (Time series) • When data are measured over equally spaced intervals of time. • line chart. Discern a pattern. 1/10/2022 Language 13

Quantitative(Cont’) • Stem and Leaf plot • Stem component • Leaf component 1/10/2022 Language 14

Quantitative(Cont’) • Frequency Histogram plot • The quantitative analogue of bar chart for qualitative • Example 1 GPA • Example 2 airline • Example 3 Discrete (weekly number of litres of milk per family) 1/10/2022 Language 15

Graph shape § Symmetric § Skewed to the right or left § Unusual observations (outliers) 1/10/2022 Language 16