Section 2.1: How to Summarize Qualitative Data Using Tables & Graphs

Section 2.1: How to Summarize Qualitative Data Using Tables & Graphs

n this module, we will consider ways to describe and represent data. We will consider frequency distributions, measures of central tendency, variances, standard deviations, percentiles, and quartiles.

Section 2.1: How to Summarize Qualitative Data Using Tables & Graphs

We will begin this section by looking at a frequency distribution. A frequency distribution is a tabular representation of the summary data which shows the numerical count of items in each class in the data set.

Look at the following data set in Table One:

Table 2.1 is a list of cars sold at The Ajax Used Car Emporium for the month of July 2014. The sales data displayed in this manner is not particularly useful to Ajax. Display the data in the form of a frequency distribution.Solution.In order to create a frequency distribution, we count the number of each model of car sold then display this information in a table. The frequency distribution for the data is shown in Table 2.2.The frequency distribution shows the number sold of each model of car. By looking at this data, Ajax can learn which brands of cars sold better than the others.

The frequency distribution tells us that the bestselling brand is Ford followed closely by Nissan.On the other hand, the brand least sold was Jeep.NOTE: For any frequency distribution, the classes must not be allowed to overlap. An overlap will result in double counting of an item and will lead to erroneous results. For some types of data, such as the car brands in example 2.1, there is usually not much chance of creating classes that overlap. However, when working with certain types of data, particularly numerical data, care must be taken to ensure that the classes do not overlap.Next, we will consider relative frequency. Relative frequency is a calculated value that represents the proportion of the items in each class. The following formula calculates the relative

frequency:

where n is the total count of all the classes being compared.The relative frequency can be converted to the relative percentage by multiplying the relative frequency by 100.Relative Percentage of a Category = Relative Frequency of a Category *100 Example 2.2 Consider the data in Table 2.1. Make a relative frequency and relative percentage distribution for this data.Solution. We have already made a frequency distribution for this data in Table 2.2. Note that Ajax sold a total of fifty cars in July 2014. Eight of the fifty sold were Chrysler In order to find the relative frequency for Chrysler, divide eight by fifty to get 8/50 = .16. The relative frequency for Ford is found by divide the of Ford’s sold, fifteen by fifty to get 15/50 = .30 and so on and so on.

In order to get the relative percentages, multiply each of the relative frequencies by 100. All of the calculations are shown Table 2.3. This table shows the calculated relative frequencies and percentages for Ajax's July 2014 car sales.

In conclusion, frequency distribution tables are a way to help us understand data numerically.While frequency distributions help us to organize and understand data numerically, charting is a means to represent frequencies visually. While there are many different types of charts available, we will focus on the following the three types of charts: the Column Chart, the Bar Chart and the Pie Chart.The basic column chart uses rectangular shapes of varying sizes to represent the different classes being evaluated. The rectangular bars for each class are lined up vertically and labeled on the x- axis of the chart. The height of each rectangle is scaled to correspond with the y-axis of the chart.Graph 2.1, which is a column chart, presents the frequency distribution of Table 2.2, in a visual format.Graph 2.1 listed the classes in alphabetical order. While the information presented in that chart is valid, it is often more helpful to arrange the data so that the class with the largest count value is

listed first and the remaining classes listed in descending order. Graph 2.2 shows the data from Table 2.2 in descending order.Listing the classes in descending order is particularly helpful to those who must look at many, many graphs. (Such a person, wants to just scan the graphs, to see which class has the highest frequency, which has the second highest, etc.) The Bar Chart is the same as the column chart except the axis are transposed - the information that was represented on the x-axis is moved to the y-axis and the y-axis is then moved to the x- axis. Graph 2.3 is the bar chart of the sorted data in Graph 2.1.