Stat Lec 4 Pt. 1 (Ch 2) PDF

CHAPTER 2 Elementary Statistics Copyright © 2010, 2007, 2004 Pearson Education, Inc. 2.1 - 1  Chapter 2 Describing, Exploring, and Comparing Data 2-1 Overview 2-2 Summarizing Data w...

CHAPTER 2 Elementary Statistics Copyright © 2010, 2007, 2004 Pearson Education, Inc. 2.1 - 1  Chapter 2 Describing, Exploring, and Comparing Data 2-1 Overview 2-2 Summarizing Data with Frequency Tables 2-3 Graphs of Data 2-4 Measures of Central Tendency 2-5 Measures of Variation 2-6 Measures of Position 2-7 Exploratory Data Analysis (EDA) Copyright © 2011 Pearson Canada Inc. 2.1 - 2  Descriptive Statistics and Inferential Statistics  Descriptive statistics summarize or describe the important characteristics of a data set.  Inferential statistics use sample data to make inferences, or generalizations, about a population. Copyright © 2011 Pearson Canada Inc. 2.1 - 3  Preview Important Characteristics of Data 1. Center: A representative or average value that indicates where the middle of the data set is located. 2. Variation: A measure of the amount that the data values vary. 3. Distribution: The nature or shape of the spread of data over the range of values (such as bell-shaped, uniform, or skewed). 90 4. Outliers: Sample values 80 70 that lie very far away 60 from the vast majority of 50 East other sample values. 40 West North 30 20 5. Time: Changing 10 characteristics of the 0 1st Qtr 2nd Qtr 3rd Qtr 4th Qtr data over time. 2.1 - 4  Shapes of Distributions Symmetric Uniform 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12 Skewed right Skewed left 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12 5 2.1 - 5  Key Concept When working with large data sets, it is often helpful to organize and summarize data by constructing a table called a frequency distribution, defined later. Because computer software and calculators can generate frequency distributions, the details of constructing them are not as important as what they tell us about data sets. It helps us understand the nature of the distribution of a data set. 2.1 - 6  Definition  Frequency Distribution (or Frequency Table) shows how a data set is partitioned among all of several categories (or classes) by listing all of the categories along with the number of data values in each of the categories. 2.1 - 7 Copyright © 2010, 2007, 2004 Pearson Education, Inc. 2.1 - 8  Tally // //// // / 10 10 Copyright © 2010, 2007, 2004 Pearson Education, Inc. 2.1 - 9  4 Steps To Organize Raw Data Into A Frequency Distribution Step 1: Decide on Number of Classes Step 2: Determine The Class Interval or width Step 3: Set The Individual Class Limits Step 4: Tally The Data Into Classes 10 2.1 - 10  Constructing a Frequency Table Step 4: Tally the vehicle selling prices into the classes. Count the number of items in each class. 11 2.1 - 11  Observed Patterns: Range: about $15,000 to about $36,000 Concentration between $18,000 & $27,000 Largest concentration is in $18,000 - $21,000 class – Typical Value = (18+21)/2 = 19.5 K. Two sold for $33,000 or more 8 sold for less than $18,000 12 2.1 - 12  Frequency Distributions Minutes Spent on the Phone 102 124 108 86 103 82 71 104 112 118 87 95 103 116 85 122 87 100 105 97 107 67 78 125 109 99 105 99 101 92 Make a frequency distribution table with five classes. Key values: Minimum value = 67 Maximum value = 125 13 2.1 - 13  Steps to Construct a Frequency Distribution 1. Choose the number of classes Should be between 5 and 15. (For this problem use 5) 2. Calculate the Class Width Find the range = maximum value – minimum. Then divide this by the number of classes. Finally, round up to a convenient number. (125 - 67) / 5 = 11.6 Round up to 12 3. Determine Class Limits The lower class limit is the lowest data value that belongs in a class and the upper class limit it the highest. Use the minimum value as the lower class limit in the first class. (67) 4. Mark a tally | in appropriate class for each data value. After all data values are tallied, count the tallies in each class for the class frequencies. 14 2.1 - 14  Construct a Frequency Distribution Minimum = 67, Maximum = 125 Number of classes = 5 Class width = 12 Class Limits Tally f 67 78 3 79 90 5 91 102 8 103 114 9 115 126 5 Do all lower class limits first. f =30 15 2.1 - 15  The Data(group work) 161 182 191 194 202 205 213 215 231 232 233 257 264 266 267 269 270 283 284 298 304 307 309 318 320 320 324 328 331 355 375 379 381 392 403 414 425 446 467 478 The data is sorted, quantitative, and there are 40 elements 2.1 - 16