CH2 | Charts & Graphs

Bar Charts or Bar Graphs

A chart that contains two or more categories along one axis and a series of bars, one for each category, along the other axis. Usually the length of the bar represents the magnitude of the measure for each category. A bar graph is qualitative and may be either horizontal or vertical.

Pie Chart

A circular depiction of data where the area of the whole pie represents 100% of the data being studied and slices represent a percentage breakdown of the sublevels.

Ogive

A cumulative frequency polygon; plotted by graphing a dot at each class endpoint for the cumulative or decumulative frequency value and connecting the dots.

Dot Plot

A dot plot is a relatively simple statistical chart used to display continuous quantitative data where each data value is plotted along the horizontal axis and is represented on the chart by a dot.

Frequency Polygon

A graph constructed by plotting a dot for the frequencies at the class midpoints and connecting the dots.

Stem-and-Leaf Plot

A plot of numbers constructed by separating each number into two groups, a stem and a leaf. The leftmost digits are the stems and the rightmost digits are the leaves.

Scatter Plot

A plot or graph of the pairs of data.

Cross Tabulation

A process for producing a two-dimensional table that displays the frequency counts for two variables simultaneously.

Cumulative Frequency

A running total of frequencies through the classes of a frequency distribution.

Frequency Distribution

A summary of data presented in the form of class intervals and frequencies.

Histogram

A type of vertical bar chart constructed by graphing line segments for the frequencies of classes across the class intervals and connecting each to the x axis to form a series of rectangles.

Pareto Chart

A vertical bar chart in which the number and types of defects for a product or service are graphed in order of magnitude from greatest to least.

Class Mark

Another name for class midpoint; the midpoint of each class interval in grouped data.

Grouped Data

Data that have been organized into a frequency distribution.

Class Midpoint

For any given class interval of a frequency distribution, the value halfway across the class interval; the average of the two class endpoints.

Ungrouped Data

Raw data, or data that have not been summarized in any way.

Range

The difference between the largest and the smallest values in a set of numbers.

Relative Frequency

The proportion of the total frequencies that fall into any given class interval in a frequency distribution.

SUMMARY

The two types of data are grouped and ungrouped. Grouped data are data organized into a frequency distribution. Differentiating between grouped and ungrouped data is important, because statistical operations on the two types are computed differently. Constructing a frequency distribution involves several steps. The first step is to determine the range of the data, which is the difference between the largest value and the smallest value. Next, the number of classes is determined, which is an arbitrary choice of the researcher. However, too few classes overaggregate the data into meaningless categories, and too many classes do not summarize the data enough to be useful. The third step in constructing the frequency distribution is to determine the width of the class interval. Dividing the range of values by the number of classes yields the approximate width of the class interval. The class midpoint is the midpoint of a class interval. It is the average of the class endpoints and represents the halfway point of the class interval. Relative frequency is a value computed by dividing an individual frequency by the sum of the frequencies. Relative frequency represents the proportion of total values that is in a given class interval. The cumulative frequency is a running total frequency tally that starts with the first frequency value and adds each ensuing frequency to the total. Two types of graphical depictions are quantitative data graphs and qualitative data graphs. Quantitative data graphs presented in this chapter are histogram, frequency polygon, ogive, dot plot, and stem-and-leaf plot. Qualitative data graphs presented are pie chart, bar chart, and Pareto chart. In addition, cross tabulation tables and two-dimensional scatter plots are presented. A histogram is a vertical chart in which a line segment connects class endpoints at the value of the frequency. Two vertical lines connect this line segment down to the x-axis, forming a rectangle. A frequency polygon is constructed by plotting a dot at the midpoint of each class interval for the value of each frequency and then connecting the dots. Ogives are cumulative frequency polygons. Points on an ogive are plotted at the class endpoints. A dot plot is a graph that displays frequency counts for various data points as dots graphed above the data point. Dot plots are especially useful for observing the overall shape of the distribution and determining both gaps in the data and high concentrations of data. Stem-and-leaf plots are another way to organize data. The numbers are divided into two parts, a stem and a leaf. The stems are the leftmost digits of the numbers and the leaves are the rightmost digits. The stems are listed individually, with all leaf values corresponding to each stem displayed beside that stem. A pie chart is a circular depiction of data. The amount of each category is represented as a slice of the pie proportionate to the total. The researcher is cautioned in using pie charts because it is sometimes difficult to differentiate the relative sizes of the slices. The bar chart or bar graph uses bars to represent the frequencies of various qualitative categories. The bar chart can be displayed horizontally or vertically. A Pareto chart is a vertical bar chart that is used in total quality management to graphically display the causes of problems. The Pareto chart presents problem causes in descending order to assist the decision maker in prioritizing problem causes. Cross tabulation is a process for producing a two-dimensional table that displays the frequency counts for two variables simultaneously. The scatter plot is a two-dimensional plot of pairs of points from two numerical variables. It is used to graphically determine whether any apparent relationship exists between the two variables.

Column Charts

Vertical bar charts.