Chapter 2.2

constructing statistical graphs

Constructing Statistical Graphs Step 1 Draw and label the x and y axes. Step 2 Choose a suitable scale for the frequencies or cumulative frequencies, and label it on the y axis. Step 3 Represent the class boundaries for the histogram or ogive, or the midpoint for the frequency polygon, on the x axis. Step 4 Plot the points and then draw the bars or lines.

constructing a relative frequency graph

Step 1: Convert each frequency to a proportion or relative frequency by dividing the frequency for each class by the total number of observations. (if there are a total of 20 frequencies, the relative frequency at each class would be x(x being frequency at point) / 20) Step 2: Find the cumulative relative frequencies. To do this, add the frequency in each class to the total frequency of the preceding class. Place these values in the column labeled Cumulative relative frequency. (An alternative method would be to find the cumulative frequencies and then convert each one to a relative frequency.) Step 3: draw the graph

Relative frequency graphs

The statistical graphs shown previously were constructed by using frequencies in terms of the raw data. These distributions can be converted to distributions using proportions instead of raw data as frequencies. These types of graphs are called relative frequency graphs. -Graphs of relative frequencies instead of frequencies are used when the proportion of data values that fall into a given class is more important than the actual number of data values that fall into that class. -To convert a frequency into a proportion or relative frequency, divide the frequency for each class by the total of the frequencies. The sum of the relative frequencies will always be 1. These graphs are similar to the ones that use raw data as frequencies, but the values on the y axis are in terms of proportions.

Pie graph

a circle that is divided into sections or wedges according to the percentage of frequencies in each category of the distribution.

stem and leaf plot

a 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.

Histogram

a graph that displays the data by using contiguous vertical bars (unless the frequency of a class is 0) of various heights to represent the frequencies of the classes.

Frequency Polygon

a graph that displays the data by using lines that connect points plotted for the frequencies at the midpoints of the classes. The frequencies are represented by the heights of the points.

ogive

a graph that represents the cumulative frequencies for the classes in a frequency distribution.

time-series graph

represents data that occur over a specific period of time. -Two data sets can be compared on the same graph (called a compound time series graph) if two lines are used,

Bar graphs

represents the data by using vertical or horizontal bars whose heights or lengths represent the frequencies of the data.

Cumulative frequency

the sum of the frequencies accumulated up to the upper boundary of a class in the distribution.

Pareto Chart

used to represent a frequency distribution for a categorical variable, and the frequencies are displayed by the heights of vertical bars, which are arranged in order from highest to lowest.