Organizing Data for Beginning Statistics
Practice problems for these concepts can be found at:
- Organizing Data Solved Problems for Beginning Statistics
- Organizing Data Supplementary Problems for Beginning Statistics
Raw data is information obtained by observing values of a variable. Data obtained by observing values of a qualitative variable are referred to as qualitative data. Data obtained by observing values of a quantitative variable are referred to as quantitative data. Quantitative data obtained from a discrete variable are also referred to as discrete data and quantitative data obtained from a continuous variable are called continuous data.
EXAMPLE 2.1 A study is conducted in which individuals are classified into one of sixteen personality types using the Myers-Briggs type indicator. The resulting raw data would be classified as qualitative data.
EXAMPLE 2.2 The cardiac output in liters per minute is measured for the participants in a medical study. The resulting data would be classified as quantitative data and continuous data.
EXAMPLE 2.3 The number of murders per 100,000 inhabitants is recorded for each of several large cities for the year 1994. The resulting data would be classified as quantitative data and discrete data.
Frequency Distribution For Quantitative
A frequency distribution for qualitative data lists all categories and the number of elements that belong to each of the categories.
EXAMPLE 2.4 A sample of rural county arrests gave the following set of offenses with which individuals were charged:
The variable, type of offense, is classified into the categories: rape, robbery, burglary, arson, murder, theft, and manslaughter. As shown in Table 2.1, the seven categories are listed under the column entitled Offense, and each occurrence of a category is recorded by using the symbol / in order to tally the number of times each offense occurs. The number of tallies for each offense is counted and listed under the column entitled Frequency. Occasionally the term absolute frequency is used rather than frequency.
Relative Frequency of a Category
The relative frequency of a category is obtained by dividing the frequency for a category by the sum of all the frequencies. The relative frequencies for the seven categories in Table 2.1 are shown in Table 2.2. The sum of the relative frequencies will always equal one.
The percentage for a category is obtained by multiplying the relative frequency for that category by 100. The percentages for the seven categories in Table 2.1 are shown in Table 2.2. The sum of the percentages for all the categories will always equal 100 percent.
A bar graph is a graph composed of bars whose heights are the frequencies of the different categories. A bar graph displays graphically the same information concerning qualitative data that a frequency distribution shows in tabular form.
EXAMPLE 2.5 The distribution of the primary sites for cancer is given in Table 2.3 for the residents of Dalton County.
To construct a bar graph, the categories are placed along the horizontal axis and frequencies are marked along the vertical axis. A bar is drawn for each category such that the height of the bar is equal to the frequency for that category. A small gap is left between the bars. The MINITAB bar graph for Table 2.3 is shown in Fig. 2-1. Bar graphs can also be constructed by placing the categories along the vertical axis and the frequencies along the horizontal axis. See Problem 2.5 for a bar graph of this type.
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