Frequency Distributions Frequency Distributions q q y y SLIDES - PDF document

Elementary Statistics Elementary Statistics Chapter 2 Chapter 2 A Step by Step Approach Sixth Edition by by Allan G. Bluman Allan G. Bluman http://www.mhhe.com/math/stat/blumanbrief http://www.mhhe.com/math/stat/blumanbrief Frequency Distributions Frequency Distributions q q y y SLIDES PREPARED SLIDES PREPARED BY BY BY BY LLOYD R. JAISINGH LLOYD R. JAISINGH and and MOREHEAD STATE UNIVERSITY MOREHEAD STATE UNIVERSITY MOREHEAD KY MOREHEAD KY Updated by Updated by Graphs Graphs Dr. Saeed Dr. Saeed Alghamdi Alghamdi King King Abdulaziz Abdulaziz University University Dr. Saeed Alghamdi, Statistics Department, Faculty of Sciences, King Abdulaziz University Objectives Notes 1-1  Organize data using frequency distributions.  …………………………………………………................  Represent data in frequency distributions graphically using histograms, frequency  ……………………………………………………............ polygons and ogives. l d i  Represent data using bar chart, Pareto chart,  ……………………………………………………............ pie graph and time series graph.  Draw and interpret a stem and leaf plot.  ……………………………………………………............  ……………………………………………………............ Dr. Saeed Alghamdi, Statistics Department, Faculty of Sciences, King Abdulaziz University Organizing Data Notes 2-2  When data are collected in original form,  …………………………………………………................ they are called raw data .  ……………………………………………………............  When the raw data are organized into a table Wh th d t i d i t t bl which called frequency distribution , the  ……………………………………………………............ frequency will be the number of values in a  ……………………………………………………............ specific class of the distribution.  ……………………………………………………............ Dr. Saeed Alghamdi, Statistics Department, Faculty of Sciences, King Abdulaziz University 1

Organizing Data Notes 2-3  A frequency distribution is the organization of  …………………………………………………................ raw data in a table form, using classes and frequencies frequencies.  ……………………………………………………............  Types of frequency distributions are  ……………………………………………………............ categorical frequency distribution , ungrouped frequency distribution and grouped frequency  ……………………………………………………............ distribution .  ……………………………………………………............ Dr. Saeed Alghamdi, Statistics Department, Faculty of Sciences, King Abdulaziz University Notes Why Construct Frequency Distributions? 2-4 To organize the data in a meaningful, intelligible way.  …………………………………………………................ To enable the reader to make comparisons among different data sets.  ……………………………………………………............ To facilitate computational procedures for measures of average and spread.  ……………………………………………………............ To enable the reader to determine the nature or shape of the distribution.  ……………………………………………………............ To enable the researcher to draw charts and graphs for the presentation of data.  ……………………………………………………............ Dr. Saeed Alghamdi, Statistics Department, Faculty of Sciences, King Abdulaziz University Categorical Frequency Distributions Notes 2-5  When the sample size (n) is large, the data  …………………………………………………................ must be grouped into categories.  ……………………………………………………............  Categorical Frequency Distributions are C t i l F Di t ib ti used for data that can be placed in specific  ……………………………………………………............ categories, such as nominal or ordinal level  ……………………………………………………............ data.  ……………………………………………………............ Dr. Saeed Alghamdi, Statistics Department, Faculty of Sciences, King Abdulaziz University 2

Categorical Frequency Distributions Notes 2-6  Example: Blood Type Frequency Distribution Blood Type Frequency Distribution  …………………………………………………................ A B B AB O O A O O B A B O AB O AB B B A A O B B O O O A O  ……………………………………………………............ Class Frequency Percent frequency f    100 100  A 6 21%  ……………………………………………………............ Total f B 8 29% f   100 % O 11 39% n  ……………………………………………………............ AB 3 11% Total 28 100% Sample Size  ……………………………………………………............ Dr. Saeed Alghamdi, Statistics Department, Faculty of Sciences, King Abdulaziz University Ungrouped Frequency Distributions Notes 2-7  Ungrouped frequency distributions are used  …………………………………………………................ for data that can be enumerated and when the range of values in the data set is small the range of values in the data set is small  ……………………………………………………............ and the sample size (n) is large.  ……………………………………………………............  Example: number of patients in the clinics  ……………………………………………………............ within a hospital.  ……………………………………………………............ Dr. Saeed Alghamdi, Statistics Department, Faculty of Sciences, King Abdulaziz University Ungrouped Frequency Distributions Notes 2-8  Example: Number of patients in the waiting rooms  …………………………………………………................ of 16 6 clinics within a hospital at a specific time. clinics within a hospital at a specific time. 5 4 4 8 Frequency Cumulative  ……………………………………………………............ Class Class Frequency Frequency % % 8 5 8 4 4 8 8 50% 4 4 8 4  ……………………………………………………............ 5 3 8+3=11 19% 5 8 4 4 8 5 11+5=16 31%  ……………………………………………………............ Total 16 ‐ 100%  ……………………………………………………............ Statistics Department, Faculty of Sciences, King Abdulaziz University 3