Statistics: The Interpretation of Data

Slides:



Advertisements
Similar presentations
Appendix A. Descriptive Statistics Statistics used to organize and summarize data in a meaningful way.
Advertisements

Introduction to Summary Statistics
Introduction to Summary Statistics
B a c kn e x t h o m e Parameters and Statistics statistic A statistic is a descriptive measure computed from a sample of data. parameter A parameter is.
1 The Islamic University of Gaza Civil Engineering Department Statistics ECIV 2305 ‏ Chapter 6 – Descriptive Statistics.
Descriptive Statistics
B a c kn e x t h o m e Classification of Variables Discrete Numerical Variable A variable that produces a response that comes from a counting process.
Chapter Two Descriptive Statistics McGraw-Hill/Irwin Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved.
Edpsy 511 Homework 1: Due 2/6.
Descriptive statistics (Part I)
Descriptive Statistics  Summarizing, Simplifying  Useful for comprehending data, and thus making meaningful interpretations, particularly in medium to.
Chapter 2 Describing Data with Numerical Measurements
Programming in R Describing Univariate and Multivariate data.
Summarizing Scores With Measures of Central Tendency
Descriptive Statistics  Summarizing, Simplifying  Useful for comprehending data, and thus making meaningful interpretations, particularly in medium to.
Basic Definitions  Statistics Collect Organize Analyze Summarize Interpret  Information - Data Draw conclusions.
Census A survey to collect data on the entire population.   Data The facts and figures collected, analyzed, and summarized for presentation and.
6.1 What is Statistics? Definition: Statistics – science of collecting, analyzing, and interpreting data in such a way that the conclusions can be objectively.
Chapter 9 Statistics Section 9.1 Frequency Distributions; Measures of Central Tendency.
Sta220 - Statistics Mr. Smith Room 310 Class #3. Section
Methods for Describing Sets of Data
2011 Summer ERIE/REU Program Descriptive Statistics Igor Jankovic Department of Civil, Structural, and Environmental Engineering University at Buffalo,
1 Excursions in Modern Mathematics Sixth Edition Peter Tannenbaum.
Introduction to Summary Statistics. Statistics The collection, evaluation, and interpretation of data Statistical analysis of measurements can help verify.
STAT 211 – 019 Dan Piett West Virginia University Lecture 1.
Chapter 2 Describing Data.
© 2011 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license.
Barnett/Ziegler/Byleen Finite Mathematics 11e1 Chapter 11 Review Important Terms, Symbols, Concepts Sect Graphing Data Bar graphs, broken-line graphs,
Chapter Eight: Using Statistics to Answer Questions.
What’s with all those numbers?.  What are Statistics?
Unit 3: Averages and Variations Week 6 Ms. Sanchez.
Descriptive Statistics Tabular and Graphical Displays –Frequency Distribution - List of intervals of values for a variable, and the number of occurrences.
Describing Data Week 1 The W’s (Where do the Numbers come from?) Who: Who was measured? By Whom: Who did the measuring What: What was measured? Where:
Statistics -Descriptive statistics 2013/09/30. Descriptive statistics Numerical measures of location, dispersion, shape, and association are also used.
Central Tendency  Key Learnings: Statistics is a branch of mathematics that involves collecting, organizing, interpreting, and making predictions from.
Slide 1 Copyright © 2004 Pearson Education, Inc.  Descriptive Statistics summarize or describe the important characteristics of a known set of population.
AP PSYCHOLOGY: UNIT I Introductory Psychology: Statistical Analysis The use of mathematics to organize, summarize and interpret numerical data.
7 th Grade Math Vocabulary Word, Definition, Model Emery Unit 4.
Chapter 4 – Statistics II
Descriptive Statistics
Methods for Describing Sets of Data
INTRODUCTION TO STATISTICS
STAT 4030 – Programming in R STATISTICS MODULE: Basic Data Analysis
BUSINESS MATHEMATICS & STATISTICS.
Chapter 2: Methods for Describing Data Sets
Chapter 6 – Descriptive Statistics
Measures of Central Tendency
Summarizing Scores With Measures of Central Tendency
Introduction to Summary Statistics
Introduction to Summary Statistics
NUMERICAL DESCRIPTIVE MEASURES
Description of Data (Summary and Variability measures)
Introduction to Summary Statistics
Numerical Descriptive Measures
Descriptive Statistics
Introduction to Summary Statistics
Introduction to Summary Statistics
HMI 7530– Programming in R STATISTICS MODULE: Basic Data Analysis
STA 291 Spring 2008 Lecture 5 Dustin Lueker.
STA 291 Spring 2008 Lecture 5 Dustin Lueker.
Introduction to Summary Statistics
Means & Medians.
Introduction to Summary Statistics
Introduction to Summary Statistics
Probability and Statistics
Chapter Nine: Using Statistics to Answer Questions
Ticket in the Door GA Milestone Practice Test
Ticket in the Door GA Milestone Practice Test
Introduction to Summary Statistics
Presentation transcript:

Statistics: The Interpretation of Data 13.1 Organizing and Representing Data 13.2 Measuring the Center and Variation of Data 13.3 Statistical Inference

13.1 Organizing and Representing Data

VISUAL REPRESENTATIONS OF DATA DOT PLOTS – used to summarize relatively small sets of data From a table - To a dot plot -

VISUAL REPRESENTATIONS OF DATA STEM AND LEAF PLOTS – also used to summarize relatively small sets of data From a table - To a stem and leaf plot -

VISUAL REPRESENTATIONS OF DATA HISTOGRAMS – data is grouped into intervals

VISUAL REPRESENTATIONS OF DATA LINE GRAPHS – also called frequency polygons

VISUAL REPRESENTATIONS OF DATA BAR GRAPHS – used with categorical data, where the horizontal scale may be some nonnumerical attribute

VISUAL REPRESENTATIONS OF DATA PIE CHARTS – represents relative amounts to a whole Percent of each tax dollar expended by Mile High School District by category

VISUAL REPRESENTATIONS OF DATA PICTOGRAPHS – useful in comparing quantities

13.2 Measuring the Center and Variation of Data

MEASURES OF CENTRAL TENDENCY MEAN – the arithmetic mean, or average MEDIAN – the middle value in a collection when the values are arranged in order of increasing size MODE – the value that occurs most frequently in a collection of values

THE MEAN The mean, or average, of a collection of values is where S is the sum of the values and n is the number of values.

THE MEAN A visual understanding using a data set of 7, 5, 7, 3, 8, and 6:

THE MEDIAN Let a collection of n data values be written in order of increasing size. If n is odd, the median, denoted by , is the middle value in the list. If n is even, is the average of the two middle values.

THE MEDIAN Data set 1: 24, 25, 25, 27, 29, 31, 32, 34, 37 Data set 2: 42, 42, 43, 44, 44, 46, 47, 47, 47, 49 average

THE MODE A mode of a collection of values is a value that occurs the most frequently. If two or more values occur equally often and more frequently than all other values, there are two or more modes. Data Set: 42, 42, 43, 44, 44, 46, 47, 47, 47, 49 The mode of this data set is 47.

MEASURES OF VARIABILITY RANGE – the difference between the smallest and largest data values QUARTILES – casually speaking, these values divide the data set into four sections, each of which contains, in increasing order, about ¼ of the data STANDARD DEVIATION – a measure of the typical deviation from the mean

DEFINITION: OUTLIER An outlier is a value that "lies outside" (is much smaller or larger than) most of the other values in a set of data. Eg. Wayne Gretzky’s statistics

DEFINITION: STANDARD DEVIATION Standard deviation is a measure of how spread out numbers are around the mean.

DEFINITION: STANDARD DEVIATION Let be the values in a set of data and let denote their mean. Then is the standard deviation.

Example 13.11 Computing a Standard Deviation Compute the mean and standard deviation for this set of data: 35 42 61 29 39

13.3 Statistical Inference

TERMINOLOGY AND NOTATION A population is a particular set of objects about which one desires information. Mean of a population = Standard deviation of a population = A sample is a subset of the population. Mean of a sample = Standard deviation of a sample =

DEFINITION: A RANDOM SAMPLE A random sample of size r is a subset of r individuals from the population chosen in such a way that every such subset has an equal chance of being chosen.

THE NORMAL DISTRIBUTION

THE 68-95-99.7 RULE FOR NORMAL DISTRIBUTIONS For a population that has a normal distribution, about 68% falls within 1 standard deviation of the mean, about 95% falls within 2 standard deviations of the mean, and about 99.7% falls within 3 standard deviations.

THE STANDARDIZED NORMAL CURVE

DEFINITION: PERCENTILE A number such that the r-th percentage of a sample or distribution is less than or equal to that number is called the r-th percentile. NOTE: Scoring at the 75th percentile on a test indicates that 75% of the students had a score less than or equal to yours, not necessarily that you got 75% of the problems correct.