Data Collection & Presentation: Methods, Tables & Visuals

TAKEAWAYS:

• Data collection uses surveys, censuses, and sampling (stratified, systematic, random) to gather accurate, cost-effective information for business decisions.
• Frequency tables organize raw data into classes, midpoints, and frequencies—critical for calculating measures like mean or skewness.
• Graphs (bar, pie, histogram) visually summarize data trends, helping managers spot patterns (e.g., Ncell’s monthly call volumes).
• Time-series data (trend, seasonal, cyclical) predicts future business performance, like NEPSE’s stock price movements.
• Qualitative vs. quantitative data: Qualitative (descriptive, e.g., customer feedback) vs. quantitative (numerical, e.g., sales figures) require different analysis tools.
• Exam focus: Master constructing frequency tables, calculating percentiles, and interpreting graphs—50% of past questions test these skills.

1. Data Collection Methods

Data is the raw material for statistics. Businesses collect data to make informed decisions, but how they collect it determines accuracy and cost.

A. Primary vs. Secondary Data

B. Methods of Data Collection

1. Census: Collects data from every member of the population.

   • Example: NEPSE’s annual survey of all listed companies.
   • Pros: Highly accurate.
   • Cons: Expensive, time-consuming (only feasible for small populations).

2. Sample Survey: Collects data from a subset of the population.

   • Types:
     • Random Sampling: Every member has an equal chance (e.g., Daraz selecting 1000 customers out of 1 million).
     • Stratified Sampling: Divides population into groups (e.g., Pathao categorizing drivers by vehicle type before sampling).
     • Systematic Sampling: Selects every nth member (e.g., NTC polling every 100th phone user).

   flowchart TD
     A["Data Collection"] --> B["Census"]
     A --> C["Sample Survey"]
     C --> D["Random"]
     C --> E["Stratified"]
     C --> F["Systematic"]

3. Observation Method: Data collected by watching behavior (e.g., recording foot traffic in Kathmandu’s Thamel).

2. Organizing Data: Frequency Tables

Raw data is meaningless without organization. Frequency tables group data into classes and count occurrences.

A. Steps to Construct a Frequency Table

1. Determine the range: $$\text{Range}=\text{Max value}-\text{Min value}$$

   • Example: For profits (in lakhs): 28, 35, 61, ..., 63 → Range = 63 – 28 = 35.

2. Choose class intervals:

   • Rule: Number of classes = $1+3.3{\log }_{10}(n)$ (where $n$ = number of observations).
   • Example: For 50 firms, $1+3.3{\log }_{10}(50)\approx 7$ classes.
   • Class width = Range / Number of classes = 35 / 7 ≈ 5 (round to 5 for simplicity).

3. Create classes:

   • Start with a lower limit slightly below the minimum value (e.g., 25–34, 35–44, etc.).

B. Worked Example: Frequency Table for Firm Profits

Given data (in lakhs): 28, 35, 61, 29, 36, 48, 59, 67, 69, 50, 48, 40, 49, 42, 41, 37, 51, 62, 63, 33, 31, 32, 35, 40, 38, 39, 60, 51, 54, 56, 6, 50, 48, 40, 49, 42, 41, 37, 51, 62, 63, 33, 31, 32, 35.

Frequency Table:

Key Terms:

• Midpoint (x): Average of class limits (e.g., (25+34)/2 = 29.5).
• Cumulative Frequency: Running total of frequencies (used for percentile calculations).

3. Data Presentation: Graphs and Charts

Visuals make data understandable. Businesses use graphs to present trends to stakeholders.

A. Types of Graphs

B. Worked Example: Bar Chart for Sales Data

Given: Sales (in 000 Rs) from 2016–2020:

Interpretation:

• Trend: Sales increased every year, with the largest jump from 2018 to 2019.
• Business Use: Helps predict 2021 sales (e.g., linear growth suggests ~95,000 Rs).

4. Time-Series Analysis

Businesses analyze past trends to forecast future performance. Time-series data has four components:

1. Trend: Long-term movement (e.g., rising smartphone sales).
2. Seasonal: Repeating patterns (e.g., Kathmandu traffic jams during Dashain).
3. Cyclical: Economic cycles (e.g., NEPSE crashes during global recessions).
4. Irregular: Random shocks (e.g., COVID-19 lockdowns).

A. Worked Example: Decomposing Time-Series Data

Given: XYZ Company’s profit (million Rs) from 2015–2023:

Analysis:

1. Trend: Overall increase (15 → 35 million Rs).
2. Seasonal/Cyclical: Dip in 2020 (likely COVID-19 impact), recovery in 2021.
3. Forecast: Using linear trend, 2024 profit ≈ 38 million Rs.

In the Real World

1. eSewa’s Transaction Trends

   • Idea Used: Time-series analysis of daily transactions to predict peak usage (e.g., during Dashain).
   • How: eSewa plots transaction volumes monthly to identify seasonal spikes (e.g., +40% in September).
   • Visual:

2. Daraz’s Sales Forecasting

   • Idea Used: Frequency tables + bar charts to categorize product sales.
   • How: Daraz groups products into classes (e.g., 0–500 Rs, 501–1000 Rs) and uses histograms to identify best-selling price ranges.
   • Example: 60% of sales fall in the 501–1000 Rs range, guiding inventory decisions.

3. NTC’s Internet Usage Reports

   • Idea Used: Pie charts to show market share.
   • How: NTC publishes pie charts of internet usage by provider (Ncell, Smart Cell, etc.) to justify infrastructure investments.
   • Visual:

4. Bank Loan Interest Calculations

   • Idea Used: Frequency distributions of loan amounts to assess risk.
   • How: Banks like NMB categorize loans into classes (e.g., 1–5 lakhs, 5–10 lakhs) and analyze default rates per class.
   • Example: Loans >10 lakhs have a 5% default rate vs. 2% for <5 lakhs.

5. Qualitative vs. Quantitative Data

Worked Example:

• Qualitative: A bank asks customers, "Why did you choose us?" Responses are coded into themes (e.g., "convenience," "low fees").
• Quantitative: The same bank tracks number of customers per branch (e.g., Branch A: 200, Branch B: 150).

Exam Tip

1. Frequency Tables:

   • Always label columns clearly (Class Interval, Midpoint, Frequency).
   • Past Question: Construct a frequency table from raw data (e.g., profits of 50 firms). Marks: 5–7.
   • Common Mistake: Forgetting to calculate midpoints or cumulative frequency.

2. Graphs:

   • Bar charts for categories (e.g., sales by product).
   • Histograms for continuous data (e.g., ages of employees).
   • Past Question: Interpret a given bar chart (e.g., "Which year had the highest sales?"). Marks: 3–5.

3. Time-Series:

   • Identify trends, seasonality, and irregularities.
   • Past Question: Forecast future values using a trend line. Marks: 5–8.

4. Data Collection:

   • Define census vs. sample survey and give real-world examples (e.g., NEPSE uses census; Daraz uses sampling).
   • Past Question: "Define stratified sampling with an example." Marks: 2–3.

5. Short-Answer Questions:

   • Qualitative data: "Define with an example." (e.g., "Customer satisfaction ratings on a scale of 1–5 are quantitative; comments like 'fast service' are qualitative.")
   • Combined mean: Use the formula: $$\text{Combined Mean}=\frac{\sum (f\times \text{Mean})}{\sum f}$$ Past Question: Calculate combined mean for groups A, B, C. Marks: 4.

Practice Questions (Exam-Style)

1. Construct a frequency table for the following data (class intervals: 10–19, 20–29, etc.): 12, 18, 22, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80.

2. Calculate the combined mean for:

   Group	Number	Mean
   A	200	25
   B	250	10
   C	300	15

3. Interpret the histogram below (imagine a histogram with 5 classes: 0–10, 10–20, ..., 40–50) and state:

   • Which class has the highest frequency?
   • Is the data skewed? If yes, how?

4. Define:

   • Systematic sampling.
   • Secondary data.

Key Formulas to Memorize

Final Checklist for Full Marks

✅ Frequency Tables: Correct classes, midpoints, and frequencies. ✅ Graphs: Accurate labels, proper graph type (bar vs. histogram). ✅ Time-Series: Identify trends/seasonality with clear reasoning. ✅ Definitions: Precise and with examples (e.g., "Stratified sampling divides population into strata like Pathao’s vehicle types"). ✅ Calculations: Show all steps (e.g., midpoint calculations).

Visual Summary:

mindmap
  root((Data Collection & Presentation))
    Primary Data
      Surveys
      Observation
    Secondary Data
      Reports
      Databases
    Sampling Methods
      Random
      Stratified
      Systematic
    Frequency Tables
      Classes
      Midpoints
      Frequencies
    Graphs
      Bar
      Pie
      Histogram
      Line
    Time-Series
      Trend
      Seasonal
      Cyclical