Organisation of Data

The full picture

Imagine the Income Tax Department receives 10 lakh tax returns in a single month. Each return has a different income figure. What do you do with 10 lakh random numbers? You cannot read them one by one. You need to organise them — group them, count them, and arrange them so that patterns jump out. That is exactly what this chapter is about: organising raw data into a form that speaks for itself.

Data comes in two broad types. Qualitative data describes a quality or category — the type of business (sole trader, partnership, company), a student's favourite subject, or whether a loan was approved or rejected. Quantitative data measures a quantity — the amount of a loan in rupees, a student's marks out of 100, or the price of petrol per litre. Quantitative data is further split into discrete data (only whole-number values, like the number of employees in a firm) and continuous data (any value within a range, like a person's weight or a shop's daily revenue). Identifying your data type is the very first step before organising it.

Once you know your data type, you can build a frequency distribution. A frequency distribution is a table that shows how often each value — or group of values — appears in your dataset. The 'group of values' is called a class interval. For example, suppose you survey 50 households in your neighbourhood about their monthly grocery spending. The amounts range from ₹2,000 to ₹8,000. Instead of listing all 50 figures, you create equal-width classes — ₹2,000–₹3,000, ₹3,000–₹4,000, ₹4,000–₹5,000, ₹5,000–₹6,000, ₹6,000–₹7,000, ₹7,000–₹8,000 — and count how many households fall into each. That count is the frequency. Instantly, you can see which spending range is most common.

There is one rule about class intervals you must get right for the board exam: the lower limit of a class is included, and the upper limit is excluded. So the class ₹3,000–₹4,000 means ₹3,000 ≤ spending < ₹4,000. A household spending exactly ₹4,000 goes into the next class (₹4,000–₹5,000), not this one. This 'lower-included, upper-excluded' convention ensures every data value belongs to exactly one class — no overlaps, no gaps.

How many class intervals should you use? Too few — say, only two intervals for data spread over ₹6,000 — and you hide important variation. Too many — say, 30 intervals — and you have barely simplified anything. The practical guideline for Class 11 is to use between 5 and 15 intervals, with all intervals having equal width. Equal width makes comparison straightforward: a bar of height 12 in one class truly means twice the frequency of a bar of height 6 in another. You find the width by dividing the range (highest value minus lowest value) by your chosen number of intervals.

Two more terms worth knowing: cumulative frequency is the running total of frequencies as you move from the first class to the last. It tells you, for instance, how many students scored below 60 out of 100. Relative frequency (or percentage frequency) is a class's frequency expressed as a percentage of the total. It helps compare distributions of different sizes — for example, the spending pattern of 50 households in Delhi versus 200 households in Kochi. These extensions of the basic frequency table come up in exam questions and build naturally on what you have just learned.

An Indian example

Priya runs a small kirana shop in Coimbatore. After Diwali she has 60 days of sales data — daily totals ranging from ₹3,200 to ₹9,800. She wants a bank loan to expand, and the loan officer asks: 'What are your typical daily sales?' Priya cannot hand over a list of 60 numbers. Instead, she organises them into a frequency distribution with six equal classes of ₹1,100 each: ₹3,200–₹4,300, ₹4,300–₹5,400, ₹5,400–₹6,500, ₹6,500–₹7,600, ₹7,600–₹8,700, ₹8,700–₹9,800. When she tallies the frequencies — 4, 8, 18, 16, 10, 4 — the table shows instantly that 34 out of 60 days (more than half) had sales between ₹5,400 and ₹7,600. The loan officer sees a consistent, healthy mid-range revenue and approves the loan. The same raw numbers that looked chaotic as a list told a persuasive story as a frequency distribution.

Key concepts covered

• Classification: qualitative, quantitative
• Frequency distribution
• Class intervals

Common misconceptions to watch for

• Wrong belief: raw data and a frequency distribution are basically the same thing, just arranged differently. Correction: they are not the same — raw data is an unorganised list where patterns are invisible, while a frequency distribution groups the data into classes and counts them, making patterns like the most common range or the spread immediately visible.
• Wrong belief: a value that falls exactly on the boundary between two classes (like ₹5,000 when classes are ₹4,000–₹5,000 and ₹5,000–₹6,000) belongs to both classes, so count it in both. Correction: by the standard convention used in NCERT, the lower limit is included and the upper limit is excluded — so ₹5,000 belongs only to the second class (₹5,000–₹6,000), never to the first.
• Wrong belief: you can use as many or as few class intervals as you like — one wide interval covering everything, or fifty tiny ones, it does not matter. Correction: the number of intervals changes what the table reveals. Too few intervals merge different values and hide variation; too many create a near-copy of the raw data with no simplification. For Class 11, aim for 5–15 equal-width intervals to strike the right balance.