Data Classification and Representation: A Statistical Overview, Slides of Statistics

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Module 1

Classifying and

Representing Data

This Photo by Unknown Author is licensed under CC BY-SA

Classifying Data

This Photo by Unknown Author is licensed under CC BY-SA

Definition: A parameter is a number

representing a population characteristic.

For instance, a class is asked to raise their

hand if they like math. 40% of the class

raises their hand. This is a parameter.

populati

on

paramet

er

Parameter Versus Statistic

Definition: A statistic is a numerical

characteristic of a sample.

For instance, voters are randomly asked

about who they will be voting for in an

upcoming election. 40% plan to vote for

candidate A. This is a statistic.

sampl

e

statisti

c

Parameter Versus Statistic

Quantitative Versus Categorical (Qualitative) Data

Data

Quantitati

ve

Continuou

s

Discrete

Qualitativ

e

• (^) Definition: Qualit ative Variables allow for classification of individuals based on an attribute/characteristic Examples:  (^) Gender  (^) State of residence  (^) Shirt color
• (^) Definition: Quant itative Variables are numerical measurements or counts of individuals (can be added/subtracted) Examples:  (^) Number of shoppers in a grocery store  (^) Length of a song  (^) Daily rainfall amounts  (^) Number of siblings Data Quantitativ e Continuou s Discrete Qualitativ e

Quantitative vs. Qualitative Data

Example 1.2: Classify each of the following as quantitative or qualitative data. If the data are quantitative, classify it as discrete or continuous. a) Jamie runs 10 laps around a track. b) The color of Jeff’s car. c) The area of a piece of property is 5. acres.

Levels of Measurements Another way to classify data is to use levels of measurement.

• (^) Nominal
• (^) Ordinal
• (^) Interval
• (^) Ratio Nomin al Ordin al Interv al Rati o

Ordinal Level Definition: The ordinal level of measurement contains data that can be ordered, but differences between data values cannot be measured (data cannot be added/subtracted). Example: Course grades A, B, C, D, or F

Interval Level Definition: The interval level of measurement contains data with a definite ordering but no 0 starting point; the differences between data values can be measured and are meaningful. Example: Years 1000, 2000, 1776, and 1492

Summary - Levels of Measurement

Nominal – categories which cannot be ordered

 Ordinal – categories which can be ordered

 Interval – can be ordered, differences are meaningful,

but no zero starting point

Ratio – can be ordered, differences are meaningful, has a zero

starting point

Levels of Measurement

Example 1.3: Classify each of the following as nominal, ordinal, interval, or ratio. a) Weights of dogs: 14, 19, 24, 30, and 34 b) Letter grades in a College Algebra class c) Years which are leap years d) The color of cars in a parking lot

Types of Graphs

 Dotplot

 Stemplot

 Pie Chart

Line Graph

 Time-series

Graph

 Bar Graph

 Pareto Chart

Dotplot

Definition: A dotplot is a number line where dots are placed above the number line to represent frequencies of data values. The dotplot below shows how many hours of sleep 15 students had the night before an exam. ● ● ● ● ● ● ● ● ● ● ● ● ● ● ● 3 4 5 6 7 8 9 Hours of Sleep