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STT 204

Business Statistics

TU BITM · Semester 3 · BITM curriculum and programme regulation

Requirement
required
Credits
3
Study Guide
9 units available

Chapter notes

Authoritative study guide across 9 syllabus units

Open a unit to read its study notes.

Unit 1: Describing Data using Graphs and Tables· 4 LHs· ~5 marks

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Part 1: Core Concepts (2 Marks)

Definition of Statistics

According to Croxton and Cowden, “Statistics may be defined as the collection, presentation, analysis, and interpretation of numerical data.”

According to Horace Secrist, “By statistics we mean aggregates of facts affected to a marked extent by multiplicity of causes, numerically expressed, enumerated or estimated In standard academic theory (reasonable), standards of accuracy, collected in a systematic manner for a predetermined purpose, and placed in relation to each other.”

Primary Data vs. Secondary Data

  • Primary Data: First-hand data collected originally by the investigator specifically for the purposeful inquiry at hand (e.g., consumer intercept surveys, direct field observations).
  • Secondary Data: Data that has already been collected, processed, and published by other agencies for some other purpose (e.g., Nepal Rastra Bank macroeconomic bulletins, Central Bureau of Statistics census reports).

Part 2: Structural Frameworks (10 Marks)

1. The Visual Data Representation Hierarchy

VISUAL PRESENTATION OF BUSINESS DATA

1. DIAGRAMMATIC (Bars) 2. GRAPHICAL (Distributions)
• Simple Bar Diagram • Histogram
• Sub-divided Bar Diagram (Finds Mode graphically)
• Multiple Bar Diagram • Frequency Polygon
• Percentage Bar Diagram • Frequency Curve (Smoothed)
• Pie Chart (Angular) • Ogives (Cumulative curves)
Angle = (Val/Tot)×360° (Finds Median & Quartiles)

2. Graphical Location of Median and Mode

  • Graphic Mode via Histogram: Locate the highest rectangle (modal class). Draw a diagonal line from the top-left corner of the modal rectangle to the top-left corner of the adjacent succeeding rectangle, and another from the top-right corner to the top-right corner of the preceding rectangle. Drop a vertical line to the horizontal XX-axis from the intersection point; the XX-coordinate is the Mode.
  • Graphic Median via Ogives: Plot both the “Less-than Ogive” and “More-than Ogive” on the same axes. Drop a perpendicular line from their intersection point to the XX-axis; the intersection point corresponds precisely to N/2N/2 and identifies the Median.

Part 3: Distinction Tables

Comparison: Diagrammatic Presentation vs. Graphical Presentation

Basis of Comparison Diagrams (Bar / Pie) Graphs (Histogram / Ogive)
Data Type Represents discrete, categorical, or qualitative attributes over space/time. Represents continuous frequency distributions and mathematical relations.
Grid Paper Requirement Drawn on plain paper; scales are illustrative. Requires precise millimeter coordinate graph paper.
Mathematical Utility Visual comparison only; cannot locate statistical parameters mathematically. Used to determine positional averages mathematically (Median, Mode, Quartiles).
Audience Target General public, corporate annual reports, board presentations. Professional statisticians, researchers, quality engineers, and economists.

Part 4: Worked Problems & Exam Traps

Numerical Archetype: Constructing Frequency Distribution & Cumulative Ogives

Problem: The weekly overtime earnings (in NPR '00) of 20 factory workers are: 12, 18, 22, 25, 30, 32, 35, 38, 41, 44, 45, 48, 50, 52, 55, 58, 62, 65, 71, 78

Required: Construct a continuous frequency distribution with equal class width of 15, and tabulate the Less-than and More-than cumulative frequencies.

Solution:

  • Lowest value = 12; Highest value = 78; Range =78−12=66= 78 - 12 = 66.
  • Class intervals: 10−25,25−40,40−55,55−70,70−8510-25, 25-40, 40-55, 55-70, 70-85.
Class Int. Frequency (f) Upper Limits Less-Than CF Lower Limits More-Than CF
10 - 25 3 Less than 25 3 More than 10 20
25 - 40 5 Less than 40 8 More than 25 17
40 - 55 6 Less than 55 14 More than 40 12
55 - 70 4 Less than 70 18 More than 55 6
70 - 85 2 Less than 85 20 More than 70 2
TOTAL N = 20 - - - -

Common Board Exam Trap: In a Less-than Ogive, cumulative frequencies are plotted against Upper Class Limits. In a More-than Ogive, cumulative frequencies are plotted against Lower Class Limits. Plotting both against class midpoints is an automatic grading error.