Chapter 2 Tabular and Graphical Methods

Cautionary comments when constructing or interpreting charts or graphs

- The simplest graph should be used for a given set of data. strive for clarity avoid unnecessary adornments. - Axes should be clearly marked with the numbers of their respective scales; each axis should be labeled. - When creating a bar char, each bar should be the same width, differing bar widths create distortions. - The vertical axis should not be given a very high value as an upper limit. Ex: A - The vertical axis should not be stretched so that an increase (or decrease) of the data appears more pronounced than warranted. Ex: B

Guidelines for constructing a frequency distribution

- classes are mutually exclusive - classes are exhaustive - the total number of classes in a frequency distribution usually ranges from 5 to 20.

Cumulative Relative Frequency Distribution:

A distribution of quantitative data recording the fraction (proportion) of observations that falls below the upper limit of each class. 1) we can sum successive relative frequencies 2) we can divide each class's cumulative frequency by the sample size.

Cumulative frequency distribution

A distribution of quantitative data recording the number of observations that falls below the upper limit of each class.

Relative Frequency Distribution: For Qualitative Data

A frequency distribution that shows the fraction (proportion) of observations in each category of qualitative data or class of quantitative data.

Relative Frequency Distribution: for Quantitative Data

A frequency distribution that shows the fraction (proportion) of observations in each category of qualitative data or class of quantitative data.

Polygon

A graph of a frequency distribution in which lines connect a series of neighboring points, where each point represents the midpoint of a particular class and its associated frequency or relative frequency. If we need to construct a Polygon we would find the midpoint for the data. ((300+400)/2)=350.

Ogive

A graph of the cumulative frequency or cumulative relative frequency distribution in which lines connect a series of neighboring points, where each point represents the upper limit of each class and its corresponding cumulative frequency or cumulative relative frequency.

Bar Chart

A graph that depicts the frequency or relative frequency of each category of qualitative data as a series of horizontal or vertical bars, the lengths of which are proportional to the values that are to be depicted.

Histograms

A graphical depiction of a frequency or relative frequency distribution; it is a series of rectangles where the width and height of each rectangle represent the class width and frequency (or relative frequency) of the respective class. the only difference between a frequency histogram and a relative frequency histogram is the units of measure.

Scatter-plot

A graphical tool that helps in determining whether or not two variables are related in some way. Each point in the diagram represents a pair of known observed values of the two variables.

Pie Chart

A segmented circle whose segments portray the relative frequencies of the categories of some qualitative variable

Frequency Distribution for Qualitative Data

A table that groups qualitative data into categories, or quantitative data into intervals called classes, where the number of observations that fall into each category or class is recorded.

Steam and Leaf Diagram

A visual method of displaying data where each value of a data set is separated into two parts: a stem, which consists of the left most digits, and a leaf, which consists of the last digit.

Classes

Intervals for a frequency distribution of quantitative data.

Define class limits that are easy to recognize and interpret

Largest value is 735 smallest value is 330 and there is 5 classes. ((735-330)/5)=81

Calculating Relative & Percent Frequencies

The relative frequency for each category in a frequency distribution equals the proportion (fraction) of observations in each category. A category's relative frequency is calculated by dividing the frequency by the total number of observations. the sum of the relative frequencies should equal one. the percent frequency for each category in a frequency distribution equals the percent (%) of observations in each category; it equals the relative frequency of the category multiplied by 100.

Frequency and Cumulative frequency Distribution for Quantitative Data

for quantitative data, a frequency distribution groups data into intervals called classes and records the number of observations that falls into each class. A cumulative frequency distribution records the number of observations that fall bellow the upper limit of each class.