Chapter 2 Review Frequency Distributions and Graphs Organizing

Chapter 2 Review Frequency Distributions and Graphs

Organizing Data • In order to describe situations, draw conclusions, or make inferences, data must be organized in a meaningful way • Done through the use of frequency distributions and statistical charts and graphs • Frequency Distribution: organization of raw data in table form, using classes and frequencies

Frequency Distribution Types • Categorical Frequency Distribution • Used when the data can be placed in specific categories, such as nominal- or ordinal-level data

Frequency Distributions cont. • Grouped Frequency Distributions • Data is grouped into classes that are more than one-unit in width • Used when the range of data values is large

Other Distribution Types • Open-Ended distribution • Frequency distribution with an open-ended class • Cumulative distribution • Distribution that shows the number of data values less than or equal to a specific value • Ungrouped Frequency distribution • Used then the range of data is small and single data values are used for each class

Properties of Freq. Distribution 1. Should be between 5 and 20 classes 2. Class width is preferably an odd number 3. Classes are mutually exclusive (non-overlapping) 4. Classes are continuous (no gaps) 5. Classes are exhaustive (contains all of the raw data) 6. Classes are equal in width (except open-ended distribution)

Constructing a Frequency Distribution 1. Determine the classes a. b. c. d. e. f. g. Find the highest and lowest values Find the range Select the number of classes desired Find the class width (divide range by # of classes desired) Select a starting point Find the upper class limits Find the boundaries 2. Tally the data 3. Find the numerical frequencies and the cumulative frequencies

Graphs and Charts • Data must be presented in graphical form after it is organized • 3 most commonly used graphs are: 1. Histogram: displays data by using contiguous vertical bars to represent the frequencies of the classes 2. Frequency Polygon: displays the data by using lines that connect point plotted for the frequency of the midpoints of the classes 3. Ogive: line graph that represents the cumulative frequencies for the classes

Examples

Other Types of Graphs • Bar Graphs: represent the data by using vertical or horizontal bars whose heights or lengths represent frequencies of the data

Other Types of Graphs cont. • Pareto charts: used to represent a frequency distribution where the bars of the chart are ordered from highest to lowest

Other Types of Graphs cont. • Pie graph: circle that is divided into sections or wedges according to the percentage of frequencies in each category of the distribution

Other Types of Graphs cont. • Time-series graph: represents data that occur over a specific period of time • Stem and Leaf plot: data plot that uses part of the data value as the stem and part of the data value as the leaf to form groups or classes

Key Words • Raw data: data in original form • Class: category that qualitative or quantitative data that raw data is placed into • Lower Class limit: smallest data value that can be included in a class • Upper class limit: largest data value included in a class • Class boundaries: separate the classes so there are no gaps in the frequency distribution

Key Words cont. • Class width: difference between the upper and lower class boundaries for each class • Class midpoint: obtained by adding the upper and lower class boundaries and dividing by 2 • Outliers: extremely large or small data values compared to the other data values