Understanding Frequency Distributions: Data Organization

Frequency Distribution

1) Loose Data: Data collected that has not been organized numerically. For example, heights of males and females obtained from a survey, arranged alphabetically.

2) Ordination: An arrangement of numerical data in ascending or descending order. The difference between the largest and smallest number is called the data range.

Example:

Data Management Data Range
2.1 1 A: 10 to 1
7.6 2 R: 9
4.9 4
8.10 6 R: range of the data.
7
8
9
10

3) Frequency Distribution: When dealing with large amounts of loose data, it's useful to distribute them into classes or categories and determine the number of individuals belonging to each category, often called a class.

A tabular distribution of data by type or category with its corresponding class frequencies is known as a frequency distribution or frequency table.

Categoría Frecuencia Rango
1-5 5
6-10 8
11-15 3
15-1 = 14 R = 14
Example:

Category or clase. Frecuencia %
20-30 17 68%
31-40 5 20%
41-50 2 8%
51-60 1 4%
Total = 25

This table is a frequency distribution of ages of 25 students from the race to prevent risks of AIEP BUSINESS INSTITUTE.

The first class includes the age category between 20 and 30, and indicates the range 20-30. Since there are 17 students in this class, the class frequency is 17.

Organizing and assembling data into classes or categories is referred to as pooled data.

Although the process of grouping data removes original details, it is advantageous because it provides a comprehensive and clear view, and clear relationships are obtained.

4) Class Interval and Class Boundary: The symbol defining a class, such as
20-30, the interval is called class. The numbers 20 and 30 are called class limits. The smallest number is the lower limit of the class, while the largest is the upper class limit. A class interval that limits the theoretically lower or upper class is called an open class interval. Example: 61 and over. Or 61 -?

5) Class Borders or True Boundaries: If measured accurately, in theory, the 60-62 class interval includes all measures from 59.5 to 62.5. These numbers are called the class border or real limits. The upper limit is called the upper boundary of the class, and the other is called the lower class boundary.

6) Size or Extent of a Class Range: The size of a class interval, designated by the letter C, is the difference between the upper and lower class borders.

C = upper boundary - lower boundary

60-62

59.5 62.5


Superior border bottom border

C = 62.5 - 59.5
C = 3

7) Class Mark or Middle Class: The class mark is the midpoint of the class, obtained by averaging the lower and upper class limits.

----
X = (60 + 62) / 2 = 61

8) Histogram and Frequency Polygon: Histograms and frequency polygons are two graphical representations of frequency distributions.

8.1) Histogram or Frequency Histogram: Consists of a set of rectangles that have:

a) Bases on the horizontal axis, marking their sites in class and length equal to the size of the class intervals.

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b) Their areas proportional to the frequency of the class.

If all class intervals are the same size, the heights of the rectangles are proportional to the frequency of the class. It is customary to take the heights numerically equal to the frequency of the class. If the class intervals are not all of equal size, the heights need to be adjusted.

8.2) Frequency Polygon: It is a line graph of the frequency of the class, drawn with respect to the class mark. It can be obtained by joining the midpoints of the tops of the rectangles of the histograms.

ni = frequency.
Ni = cumulative frequency: e.g., 8 + 10 = 18, 18 + 16 = 34.
fi = ni = 1 e.g., 8 / 65 = 0.12, 10 / 65 = 0.15
N
Fi = 0.12 + 0.15 = 0.27, 0.27 + 0.25 = 0.52.
fi x 100% = 0.12 x 100 = 12, 0.15 x 100 = 15
Fi x 100% = 0.12 x 100 = 12, 0.27 x 100 = 27