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Unformatted text preview: Chapter 1 Descriptive Statistics 1.1 What is Statistics? Statistics is the science of collecting, summarizing and analyzing data that are subject to random variation. Statistics → Data collection Data analysis Data collection → experimental design survey sampling observational study Data analysis → descriptive statistics statistical inference estimation testing hypothesis 11 1.2 Basic Terms Definition 1.1 Population – A collection of all possible individuals, objects, or measurements of interest Definition 1.2 Sample – A selected subset of a population. The sample is intended to give representative results of the population from which it was selected. Total number of units in a sample is called the sample size , denoted by n . Example 1.1 The following table provides information on the floor level , age , size , sales prices , and prices per square feet for 10 residential properties sold in last month. Each row of the data set pertains to a single residential property and gives the following information: x 1 Floor level (High, Medium, Low) x 2 District (HK, KLN, NT) x 3 Age (in years) x 4 Size (square feet) x 5 Sale price (in ten thousand dollars) x 6 Price per square feet Property x 1 x 2 x 3 x 4 x 5 x 6 1 High NT 13 732 322 4399 2 Low HK 9.5 766 299 3903 3 Low NT 13 583 250 4288 4 Medium HK 23 612 350 5719 5 High NT 6 910 550 6044 6 Low HK 16 2404 1150 4784 7 High HK 12.5 1907 1410 7394 8 Medium KLN 10 797 340 4266 9 High KLN 14 1471 920 6254 10 Low KLN 6.5 798 292 3659 12 Definition 1.3 An element or member of a sample or population is a specific subject or object about which the information is collected. Definition 1.4 Variable – A characteristic of an element There are two basic types of variables: • Qualitative variable (Categorical variable) – places an individual into one of several groups or categories • Quantitative variable – takes numerical values for which arithmetic operations make sense Definition 1.5 The value of a variable for an element is called an observation or measurement . Definition 1.6 A data set is a collection of observations on one or more variables. 13 1.3 Graphical Presentation for Qualitative Variable Example 1.2 14 A sample of 50 New Car Purchases 15 Example 1.3 Gas consumption values in a particular quarter from 100 households 55 82 83 109 78 87 95 94 85 67 80 109 83 89 91 104 90 103 67 52 107 78 86 19 72 66 92 99 60 75 88 112 97 88 49 62 70 66 88 62 72 85 81 78 77 41 105 92 94 74 78 75 87 83 71 99 56 69 78 60 119 39 104 86 67 79 98 102 82 91 46 120 73 62 68 86 70 55 112 83 62 74 99 100 86 67 61 97 77 59 65 51 99 53 105 95 107 46 90 71 2 • Categorizing the data, k – the number of classes • Frequency: Count the no. of elements belonging to each of the categories, denoted by f i for the i th category • Relative Freqency: Relative Freq of i th Category = Freq of that category Sum of all freq = f i /n , where n is the total number of elements • Percentage:...
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This note was uploaded on 09/24/2010 for the course MATH 144 taught by Professor Lisiufeng during the Fall '09 term at HKUST.
 Fall '09
 lisiufeng
 Math, Statistics

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