Chapter 2 Frequency Distribution and Graph Instructor: Alaa saud Note: This PowerPoint is only a summary and your main source should be the book. Note: This PowerPoint is only a summary and your main source should be the book.

Outline 2-1 Organizing Data 2-2 Histogram , Frequency Polygons, and Ogives 2-3 Other Types of Graphs Summary Note: This PowerPoint is only a summary and your main source should be the book.

2-1 Organizing Data When data are collected in original form, they are called raw data. 49 57 38 73 81 74 59 76 65 69 54 56 69 68 78 65 85 49 69 61 48 81 68 37 43 Researcher organize raw data in table form called a frequency distribution , that consists of classes and frequencies. Note: This PowerPoint is only a summary and your main source should be the book.

Types of Frequency Distributions Categorical frequency distributions Grouped Frequency Distributions Note: This PowerPoint is only a summary and your main source should be the book.

Categorical frequency distributions Categorical frequency distributions: can be used for data that can be placed in specific categories, such as nominal- or ordinal-level data. Examples: blood type… Note: This PowerPoint is only a summary and your main source should be the book.

Example: 25 Army inductees were given a blood test to determine their blood type. The data set is : A B B AB O O O B AB B B B O A O A O O O AB AB A O B A Note: This PowerPoint is only a summary and your main source should be the book.

IIII IIII II IIII IIII % = A 5 20 0.20 B 7 28 0.28 O 9 36 0.36 AB |||| CLASS TALLY FREQUENCY (f) PERCENT Relative frequency A 5 20 0.20 B 7 28 0.28 O 9 36 0.36 AB |||| 4 16 0.15 n=25 100 1 IIII IIII II IIII IIII Note: This PowerPoint is only a summary and your main source should be the book.

Grouped frequency distributions Grouped frequency distributions: can be used when the range of values in the data set is very large. The data must be grouped into classes that are more than one unit in width. Examples - the life of boat batteries in hours. Note: This PowerPoint is only a summary and your main source should be the book.

Grouped Frequency Distributions Upper boundary Lower boundary Upper limit Lower limit Class limits Class boundaries Tally Frequency 24-30 23.5-30.5 /// 3 31-37 30.5-37.5 / 1 38-44 37.5-44.5 //// 5 45-51 44.5-51.5 //// //// 9 52-58 51.5-58.5 //// / 6 59-65 58.5-65.5 Note: This PowerPoint is only a summary and your main source should be the book.

Class Limits Lower class limit Upper class limit Class Boundaries Lower boundary limit Upper boundary limit Note: This PowerPoint is only a summary and your main source should be the book.

Terms Associated with a Grouped Frequency Distribution Class limits: represent the smallest and largest data values that can be included in a class. In the lifetimes of boat batteries example, the values 24 and 30 of the first class are the class limits The lower class limit is 24 and the upper class limit is 30. Note: This PowerPoint is only a summary and your main source should be the book.

Lower boundary= lower limit - 0.5 Upper boundary= upper limit + 0.5 Class boundaries :The class boundaries are used to separate the class so that there is no gaps in frequency distribution. Lower boundary= lower limit - 0.5 Upper boundary= upper limit + 0.5 Note: This PowerPoint is only a summary and your main source should be the book.

Lower boundary= lower limit - 0.05 =7.8-0.05 =7.75 Class limits should have the same decimal place value as the data, but the class boundaries should have one additional place value and end in a 5. For example Class limit Class boundary 7.8-8.8 7.75-8.85 Lower boundary= lower limit - 0.05 =7.8-0.05 =7.75 Upper boundary= upper limit + 0.05 =8.8+0.05=8.85 Note: This PowerPoint is only a summary and your main source should be the book.

Example: Find the class boundaries for each class ? A. 2.67 – 3.93 B. 49.005

The class width for a class in a frequency distribution is found by subtracting the lower (or upper) class limit of one class minus the lower (or upper) class limit of the previous class Class width=lower of second class limit-lower of first class limit Or Class width=upper of second class limit-upper of first class limit For example: Class limits Class boundaries 24-30 23.5-30.5 31-37 30.5-37.5 Class width=31-24=7 Class width=30.5-23.5=7 Note: This PowerPoint is only a summary and your main source should be the book.

The class midpoint Xm is found by adding the lower and upper class limit (or boundary) and dividing by 2 . Xm = Or Xm = Class limits Class boundaries 24-30 23.5-30.5 31-37 30.5-37.5 For example : Note: This PowerPoint is only a summary and your main source should be the book.

Guidelines for Constructing a Frequency Distribution There should be 5-20 classes. The class width should be an odd number. The classes must be mutually exclusive. The classes must be continuous. The classes must be exhaustive. The classes must be equal in width (except in open-ended distributions). Age 10-20 20-30 30-40 40-50 Age 10-20 21-31 32-42 43-53 A better way to construct a frequency distribution Note: This PowerPoint is only a summary and your main source should be the book.

Procedure for Constructing a Grouped Frequency Distribution STEP 1:Determine the classes : Find the highest and lowest value. Find the range. Select the number of classes desired. Find the width by dividing the range by the number of classes and rounding up. Select a starting point (usually the lowest value); add the width to get the lower limits. Find the upper class limits. Find the boundaries. STEP 2: Tally the data. STEP 3: Find the frequencies and find the cumulative frequency. Note: This PowerPoint is only a summary and your main source should be the book.

Example: 1- The following data represent the record high temperatures for each of the 50 states. Construct a grouped frequency distribution for the data using 7 classes. 112 100 127 120 134 118 105 110 109 112 110 118 117 116 118 122 114 114 105 109 107 112 114 115 118 117 118 122 106 110 116 108 110 121 113 120 119 111 104 111 120 113 120 117 105 110 118 112 114 114 Note: This PowerPoint is only a summary and your main source should be the book.

1- Range= High-Low=134-100=34 2-class width Range of data is large 1- Range= High-Low=134-100=34 2-class width Note: This PowerPoint is only a summary and your main source should be the book.

112 100 127 120 134 118 105 110 109 112 110 118 117 116 118 122 114 114 105 109 107 112 114 115 118 117 118 122 106 110 116 108 110 121 113 120 119 111 104 111 120 113 120 117 105 110 118 112 114 114 Class Limits 100 - 104 105 - 109 110 - 114 115 - 119 120 - 124 125 - 129 130 - 134 Class Boundaries Frequency Cumulative Frequency 99.5 - 104.5 104.5 - 109.5 109.5 - 114.5 114.5 - 119.5 119.5 - 124.5 124.5 - 129.5 129.5 - 134.5 2 8 18 13 7 1 2 10 28 41 48 49 50 Note: This PowerPoint is only a summary and your main source should be the book.

2 10 28 41 48 49 50 Less than 99.5 Less than 104.5 Less than 109.5 Cumulative Frequency 2 10 28 41 48 49 50 Less than 99.5 Less than 104.5 Less than 109.5 Less than 114.5 Less than 119.5 Less than 124.5 Less than 129.5 Less than 134.5 Note: This PowerPoint is only a summary and your main source should be the book.

Exercise In a survey of 20 patients who smoked, the following data were obtained. Each value represents the number of cigarettes the patient smoked per day. Construct a frequency distribution using six classes. Note: This PowerPoint is only a summary and your main source should be the book.