Organisation of Data

The full picture

Imagine the Kerala Bureau of Statistics has just finished a survey: 200 fish-landing centres, each reporting daily catch in kilograms. You now have 200 numbers scribbled in no particular order. Can you tell at a glance whether most landings are small or large? No — because the data is raw. Raw data is simply an unordered collection of observations. Organisation of data is the process of sorting and grouping those observations so patterns jump out. This is always the first step before any statistical analysis.

The first decision in organising data is identifying what kind of data you have. Qualitative data (also called attributes) describes characteristics that cannot be measured — the type of fish (sardine, tuna, pomfret), or the fishing method used (trawl, purse seine, hook-and-line). You cannot add or subtract these; you can only count how many observations fall in each category. Quantitative data, on the other hand, involves actual numbers — kilograms caught, price per kilogram in rupees, number of workers. Quantitative data divides further: discrete data takes only whole number values (3 boats, 12 workers), while continuous data can take any value in a range (47.3 kg, ₹182.50 per kg).

Once you know your data type, you build a frequency distribution. This is a table that groups observations into classes and records how many observations fall in each class — that count is the frequency. For example, take daily wages of 80 agricultural labourers in Thrissur district: instead of listing all 80 figures, you create groups like ₹400–500, ₹500–600, ₹600–700, ₹700–800, and count how many workers fall in each. You now have a compact picture of the wage structure at a glance. The range covered by each group is the class interval, and its width is the class width.

Choosing the right number of classes is a judgment call — a useful starting point is the square-root rule: number of classes ≈ √N, where N is the total number of observations. For 100 observations, try about 10 classes. Too few classes (say, 3) lump everything together and hide variation; too many (say, 50) scatter the data into near-empty boxes. Equal class widths are almost always preferred because they make comparison and later graphing straightforward. Unequal widths and open-ended classes (such as 'below ₹5,000' or 'above ₹50,000') are used only when data is very sparse at the extremes.

The exclusive method is the standard way to handle boundaries between classes in economics. In this method, the upper limit of each class is excluded — it belongs to the next class. If your classes are ₹500–600 and ₹600–700, an observation of exactly ₹600 goes into ₹600–700, not ₹500–600. This rule is simple and completely eliminates the problem of where to put boundary values. Every observation falls into exactly one class, with no overlaps and no gaps. Always use this method unless your textbook specifically instructs otherwise.

Constructing a frequency distribution table follows a clear sequence: (1) find the highest and lowest values to know your range; (2) decide how many classes you need using the square-root guideline; (3) calculate class width as range ÷ number of classes, then round to a convenient figure; (4) list the class intervals from lowest to highest; (5) tally each observation into its class; (6) write the frequency for each class. You can also add a relative frequency column showing each class's frequency as a percentage of total observations — this makes comparisons across datasets of different sizes fair and easy.

An Indian example

Meera runs a small wholesale fish market in Kozhikode. In one month she records the daily sale value (in rupees) for 60 trading days. The values range from ₹8,000 on slow monsoon days to ₹72,000 on peak festival days. Before she can understand her business, she groups these 60 figures into classes: ₹0–12,000 (4 days), ₹12,000–24,000 (9 days), ₹24,000–36,000 (17 days), ₹36,000–48,000 (19 days), ₹48,000–60,000 (8 days), ₹60,000–72,000 (3 days). Now the picture is clear: nearly 60% of days cluster in the ₹24,000–48,000 band — her reliable income zone. The few very high days (₹60,000+) are rare festival spikes, not the norm. She uses this organised table to decide when to hire extra staff and how much stock to order on average. Sixty raw numbers told her nothing; one frequency distribution told her everything she needed.

Common misconceptions to watch for

• Misconception: An observation that falls exactly on the boundary of two classes can go into either class. Correction: Under the exclusive method — which is standard in economics — the upper boundary is excluded from each class. So an observation of exactly ₹600 belongs to the class starting at ₹600, not the class ending at ₹600. There is no ambiguity.
• Misconception: You must always use exactly √N classes — it is a formula, not a guideline. Correction: The square-root rule is a starting point, not a law. For 64 observations it suggests 8 classes, but if your data is tightly clustered you might use 6, or if it is very spread out you might use 10. The goal is a table that clearly shows the shape of the data.
• Misconception: Qualitative data like crop type or fishing method needs to be converted to numbers (1 = rice, 2 = wheat, etc.) before you can organise it. Correction: No conversion is needed. You simply count how many observations belong to each named category and record those counts in a frequency table. Assigning arbitrary numbers to categories would imply a numerical relationship (is rice 'twice' wheat because 2 > 1?) that does not exist.