Data Description Data Description p SLIDES PREPARED SLIDES - PDF document

Elementary Statistics Elementary Statistics Chapter 3 Chapter 3 A Step by Step Approach Sixth Edition by by Allan G. Allan G. Bluman Bluman http://www.mhhe.com/math/stat/blumanbrief http://www.mhhe.com/math/stat/blumanbrief Data Description Data Description p SLIDES PREPARED SLIDES PREPARED BY BY BY BY LLOYD R. JAISINGH LLOYD R. JAISINGH MOREHEAD STATE UNIVERSITY MOREHEAD STATE UNIVERSITY MOREHEAD KY MOREHEAD KY Updated by Updated by Dr. Saeed Dr. Saeed Alghamdi Alghamdi King Abdulaziz King Abdulaziz University University www.kau.edu.sa/saalghamdy www.kau.edu.sa/saalghamdy Dr. Saeed Alghamdi, Statistics Department, Faculty of Sciences, King Abdulaziz University Objectives Notes 3-1 � Summarize data using measures of central � …………………………………………………................ tendency, such as the mean, median, mode, and midrange. � ……………………………………………………............ � Describe data using the measures of variation, such as the range, variance, and � ……………………………………………………............ standard deviation. � ……………………………………………………............ � ……………………………………………………............ Dr. Saeed Alghamdi, Statistics Department, Faculty of Sciences, King Abdulaziz University Objectives Notes 3-2 � Identify the position of a data value in a � …………………………………………………................ data set using various measures of position, such as standard scores and quartiles. q � ……………………………………………………............ � Use the techniques of exploratory data � ……………………………………………………............ analysis, including boxplots and five- number summaries to discover various � ……………………………………………………............ aspects of data. � ……………………………………………………............ Dr. Saeed Alghamdi, Statistics Department, Faculty of Sciences, King Abdulaziz University 1

Introduction Notes 3-3 � Statistical methods can be used to summarize � …………………………………………………................ data. � Measures of average are also called measures � ……………………………………………………............ of central tendency and include the mean , f t l t d d i l d th median , mode , and midrange . � ……………………………………………………............ � Measures that determine the spread of data values are called measures of variation or � ……………………………………………………............ measures of dispersion and include the range , variance , and standard deviation . � ……………………………………………………............ Dr. Saeed Alghamdi, Statistics Department, Faculty of Sciences, King Abdulaziz University Introduction Notes 3-4 � Measures of position tell where a specific data value � …………………………………………………................ falls within the data set or its relative position in comparison with other data values. � ……………………………………………………............ � The most common measures of position are standard scores and quartiles . � ……………………………………………………............ � The measures of central tendency, variation, and position are part of what is called traditional � ……………………………………………………............ statistics . � ……………………………………………………............ Dr. Saeed Alghamdi, Statistics Department, Faculty of Sciences, King Abdulaziz University Introduction Notes 3-5 � Another type of statistics is called exploratory � …………………………………………………................ data analysis which include the box plot and the five-number summary . � ……………………………………………………............ � A statistic is a characteristic or measure obtained by using the data values from a � ……………………………………………………............ sample. � A parameter is a characteristic or measure � ……………………………………………………............ obtained by using all the data values for a specific population. � ……………………………………………………............ Dr. Saeed Alghamdi, Statistics Department, Faculty of Sciences, King Abdulaziz University 2

Measures of Central Tendency Notes 3-6 � The mean is the sum of the values divided by � …………………………………………………................ the total number of values. � The Greek letter μ (mu) is used to represent � ……………………………………………………............ th the population mean. l ti ∑ + + + X X X .... X μ = = 1 2 N � ……………………………………………………............ N N � The symbol (“x-bar”) represents the sample x ∑ mean. � ……………………………………………………............ + + + x .... x x x = = 1 2 n x n n � ……………………………………………………............ Dr. Saeed Alghamdi, Statistics Department, Faculty of Sciences, King Abdulaziz University Measures of Central Tendency Notes 3-7 � Example: Suppose that the number of burglaries reported for a specific year for nine communities are � …………………………………………………................ 61, 11, 1, 3, 2, 30, 18, 3, 7 Find the mean Find the mean. � ……………………………………………………............ ∑ + + + + + + + + n = 61 11 1 x 3 2 30 18 3 7 136 = X = = 15.1 � ……………………………………………………............ 9 9 � ……………………………………………………............ * See examples 3-1 and 3-2 � ……………………………………………………............ Dr. Saeed Alghamdi, Statistics Department, Faculty of Sciences, King Abdulaziz University Measures of Central Tendency Notes 3-8 � The median is the halfway point in a data set. The symbol for the median is MD. � …………………………………………………................ � The median is found by arranging the data in order and selecting the middle point. g p � ……………………………………………………............ � Example: Suppose that the number of burglaries reported for a specific year for nine communities are � ……………………………………………………............ 61, 11, 1, 3, 2, 30, 18, 3, 7 Find the median. � ……………………………………………………............ MD: 1, 2, 3, 3, 7, 11, 18, 30, 61 , So MD= 7 * See examples 3-4, 3-5, 3-6 and 3-8 � ……………………………………………………............ Dr. Saeed Alghamdi, Statistics Department, Faculty of Sciences, King Abdulaziz University 3