Collection, Classification and Presentation of Data

Definition: Statistical data are numerical facts collected for a purpose. By source they are primary (collected first-hand by the investigator) or secondary (already collected by someone else and reused).

Primary vs Secondary

• Primary data — original, collected for the current study (surveys, direct interviews, questionnaires, observation). More reliable but costly and slow.
• Secondary data — from published sources (census reports, government publications, journals). Cheap and quick, but may not fit exactly and needs scrutiny for reliability.

Methods of Collecting Primary Data

Direct personal interview, indirect oral investigation, mailed questionnaires, schedules sent through enumerators, and telephone interviews.

Real-world example: A researcher surveying households directly collects primary data; using the national Census figures for the same area is using secondary data.

Example 1. Data collected first-hand by an investigator for their own study is called:

• Primary data.

Example 2. Census reports used by a researcher for a new study are an example of:

• Secondary data.

Example 3. Which method uses enumerators to fill schedules at the respondent's location?

• Schedules through enumerators (a primary-data method).

Definition: Classification groups raw data into homogeneous classes by a common characteristic; tabulation then arranges the classified data into rows and columns.

Bases of Classification

• Quantitative (by magnitude — e.g. income classes), Qualitative (by attribute — e.g. gender), Geographical (by region), Chronological (by time).

Parts of a Table

Title, stub (row headings), caption (column headings), body, head-note and foot-note.

Frequency Distribution

Data grouped into class intervals with their frequencies; may be discrete or continuous, and shown as a cumulative frequency (less-than / more-than) distribution.

Real-world example: Grouping exam scores into 0–10, 10–20 … bands with counts is a continuous frequency distribution.

Example 1. Classifying data by region (state-wise) is which type of classification?

• Geographical.

Example 2. In a statistical table, the column headings are called the:

• Caption.

Example 3. A distribution showing the count of values "less than" each class boundary is a:

• Cumulative frequency distribution.

Definition: Diagrammatic and graphical presentation displays data visually so comparisons and trends are immediately clear.

Diagrams (for comparison)

Bar diagrams (simple, multiple, sub-divided), pie charts, and pictograms.

Graphs (for frequency distributions)

• Histogram — bars for continuous class intervals.
• Frequency polygon — line joining midpoints of histogram tops.
• Ogive — cumulative frequency curve (less-than / more-than); their intersection gives the median.

Real-world example: An ogive lets you read off the median and quartiles graphically, without direct calculation.

Example 1. The cumulative frequency curve is known as an:

• Ogive.

Example 2. The point where the "less-than" and "more-than" ogives intersect gives the:

• Median.

Example 3. A frequency polygon is formed by joining the ______ of the tops of histogram bars.

• Midpoints.