Chapter 24: Data Handling (Statistics)

1. Introduction to Statistics and Data

• Definition of Statistics: The term is used in two senses:
  • Singular sense: The subject or branch of knowledge dealing with collecting, analyzing, presenting, and interpreting numerical data.
  • Plural sense: The collection of numerical data with a definite object in view (e.g., population statistics, tax data).
• Data: A set of numerical facts collected with a specific objective.
• Tabulation: The systematic arrangement of data, generally in the form of a table, to make it easier to understand.
• Frequency: A number that tells how many times a particular data point (observation) appears in a given set.

2. Organization of Data

• Raw Data: Data recorded in its original form as it is collected.
• Arrayed Data (Array): Data arranged in ascending or descending order of magnitude.
• Frequency Distribution: A tabular arrangement showing the frequency of each number or observation.
• Constructing a Table:
  • Data is often organized using a "Tally Marks" column.
  • Tally marks are grouped in bundles of five (four vertical strokes crossed by a diagonal stroke).

3. Grouped Frequency Distribution

• Class-Interval: When data is large, it is grouped into ranges (e.g., 10-20, 20-30).
• Class Limits: The boundaries of a class interval.
  • Lower Class Limit: The smaller number in the interval (e.g., 10 in 10-20).
  • Upper Class Limit: The larger number in the interval (e.g., 20 in 10-20).
• Class Mark: The value midway between the lower and upper class limits.

4. Graphical Representation: Bar Graphs

• Bar Graph (Bar Chart): A visual representation using rectangular bars of equal width.
• Properties:
  • The width of the bars does not represent any value; only the height represents the data.
  • The heights are directly proportional to the frequency or value they represent.
  • Equal space must be left between consecutive bars.
• Double Bar Graph: Two bar graphs drawn side-by-side to compare two collections of data (e.g., comparing the number of boys and girls in different classes).

5. Graphical Representation: Pie Charts

• Pie Graph (Pie Chart): Numerical data represented by the sectors of a circle.
• Sector: The region of the circle enclosed by two radii and an arc.
• Central Angle: The angle formed at the center of the circle by the two radii of a sector. The sum of all angles about the center is 360°.
• Construction: To draw a pie chart, the value of each component is converted into a proportionate angle.