What is discrete frequency distribution?

1. Classification of data:

Arrangement of the primary data in a definite pattern.

2. Types of Classification:

(i) Classification by time or Chronological classification: Classification of data according to time.

(ii) Classification by Space (Spatial) or Geographical Classification: Classification of data with reference to geographical location.

(iii) Classification by attributes or Qualitative classification: Classification of statistical data on the basis of attribute.

(iv) Classification by Size or Quantitative Classification: Classification of data on the basis of their magnitude.

3. Tabulation:

A logical step after classifying the statistical data is to present them in the form of tables.

4. Types of Tables:

(i) General tables: It contains a collection of detailed information.

(ii) Summary tables: Tables, emphasize on required aspect of data.

5. Components of a Table:

(i) Table Number and Title: Number and title given to a table based on the data represented.

(ii) Stub: A for brief and self-explanatory headings of rows.

(iii) Caption: Brief and self-explanatory headings of columns.

(iv) Body of the Table: It provides the numerical information in different cells.

(v) Footnote: The explanatory notes to understand the data at a later stage.

(vi) Source of Data: It refers the original data.

6. Frequency Distribution:

A tabular arrangement of raw data by a certain number of classes and the number of items belonging to each class.

(i) Discrete Frequency Distribution: Arrangement of raw data containing a limited number of values and each of them appeared many numbers of times.

(ii) Continuous Frequency Distribution: Large mass of data summarized by distributing the data into groups, or classes, or categories with the frequencies.

(iii) Cumulative Frequency Distribution: A tabular arrangement of all cumulative frequencies together with the corresponding classes.

(a) Less than cumulative frequency distribution: Cumulative frequency for each class showing the number of elements with magnitudes less than the upper limit.

(b) More than Cumulative Frequency Distribution: Cumulative frequency for each class showing the number of elements with magnitudes larger than the lower limit.

(iv) Relative-Cumulative Frequency Distributions: The ratio of the cumulative frequency to the total frequency.

(v) Bivariate Frequency Distributions: Frequency distribution of two variables.

7. Terms related to frequency distribution:

(i) Class: Data set divided into groups bounded by limits.

(ii) Class limits: The end values of a class.   

(iii) Class interval: Upper limit $-$ Lower limit

(iv) Class boundaries: The midpoints between the upper limit of a class and the lower limit of its succeeding class.

(v) Width of a class: Upper class boundary $-$ Lower class boundary.

(vi) Methods of formation of frequency distribution:

(a) Inclusive method: Both the lower and upper class limits are included in the classes.

(b) Exclusive method: Upper limit of a class is included in the next class.   

8. True class intervals:

In the case of continuous variables, we take the classes in such a way that there is no gap between successive classes.

9. Open End Classes:

A class limit is missing either at the lower end of the first class interval or at the upper end of the last classes or when the limits are not specified at both the ends.

10. Stem and Leaf Plot (Stem and Leaf Diagram):

(i) Stem is the label for left digit (leading digit) and leaf is the label for the right digit (trailing digit) of a number.

(ii) Using a Stem and Leaf plot, finding the Mean, Median, Mode and Range:

(a) The mean $=\frac{\text{Sum of all the values}}{\text{Number of values}}$

(b) The median: The data value in the middle when the data is ordered from the smallest to the largest.

(c) The mode: The data value that occurs most often.

(d) The range: The difference between the highest and the least data value.