Presentation of Data

The full picture

Imagine you survey 50 students about their daily mobile data usage and get back 50 random numbers. No one can make sense of a list. Data presentation is the process of arranging those numbers into tables, charts, and curves so that a reader — your teacher, a business owner, a government official — can spot patterns at a glance. NCERT groups all these methods into two broad families: tabular presentation (rows and columns) and diagrammatic presentation (charts and curves).

A frequency table is your starting point. You sort data into class intervals — say, 0–1 GB, 1–2 GB, 2–3 GB — and count how many values fall into each. That count is the frequency. Add a third column that keeps a running total and you have cumulative frequency, which answers questions like 'how many students use less than 2 GB?' Tables give exact numbers, which is great when precision matters. Their weakness is that trends and comparisons are harder to see at a glance — that is where diagrams step in.

Bar diagrams are the simplest diagram. Draw vertical bars whose heights match the frequencies of different categories. Because the categories are separate (brands, subjects, years), there are gaps between bars. They are perfect for comparing — 'which brand sold the most?' Pie charts go further: they slice a circle into sectors where each sector's angle is proportional to its share of the total (formula: value ÷ total × 360°). A pie chart answers 'what fraction?' rather than 'how many?', so use it when composition matters — say, how your family's monthly budget of ₹40,000 is split between rent, food, and transport. Pie charts work best when there are five or six categories at most; beyond that, the slices become too thin to read clearly.

When data is continuous — like heights, weights, or income ranges — you use a histogram. Continuous means there are no natural gaps; a student who is 162.7 cm tall is just as valid as one who is 163 cm. Because the intervals flow into each other, histogram bars touch. Bar height equals frequency when all intervals are equal in width (the standard case in NCERT Class 11). Once you have a histogram, join the midpoints of the tops of each bar with straight lines and you get a frequency polygon, which shows the shape of the distribution — whether most values cluster at one end or in the middle.

An ogive (say it: OH-jive) is a cumulative frequency curve. Instead of plotting frequency at each midpoint, you plot the running total of frequencies at the upper boundary of each class. Because you keep adding, the curve can never go down — it always rises (or flattens, but never falls). The ogive is powerful because you can use it to read off the median visually: find the point at n/2 on the y-axis, trace across to the curve, then drop to the x-axis. For a board exam question asking you to estimate the median from a curve, the ogive is your tool.

Choosing the right diagram is as important as drawing it correctly. Use bar diagrams for comparing separate categories. Use pie charts for showing proportions among a small number of categories (five or six at most). Use histograms for continuous data. Use frequency polygons when you want to compare two distributions on the same graph. Use ogives when you need to answer 'how many up to a certain value?' or find the median. Getting this matching right often earns you a mark on its own in the board paper.

An Indian example

Priya runs a small kirana store in Kochi. She records the daily sales for 60 days: some days she earns ₹1,500, other days ₹4,800, most days somewhere in between. She groups the data into classes — ₹1,000–₹2,000, ₹2,000–₹3,000, ₹3,000–₹4,000, ₹4,000–₹5,000 — and counts how many days fell into each. The frequency table shows at a glance that 26 out of 60 days, her earnings were ₹2,000–₹3,000 — that is her modal class, and it tells her what a 'typical' day looks like. She draws a histogram to see that her earnings are slightly skewed toward the lower end; most days are average, but a few busy festival days pull the tail rightward. Then she draws an ogive. By tracing to the 30th day (n/2 = 30) on the curve, she finds her median daily sales are about ₹2,600. She now knows: half her days earn below ₹2,600. That single number tells her she needs to either push sales on slow days or cut costs to stay profitable.

Key concepts covered

• Tabular & diagrammatic presentation
• Bar diagrams, pie, histograms, frequency polygons, ogives

Common misconceptions to watch for

• Wrong belief: 'A histogram is just a bar chart where the bars happen to touch.' Correction: The touching bars are not a style choice — they signal that the data is continuous (no gaps between values are possible). Bar charts use gaps to show that their categories are discrete and separate. If you draw a histogram for categorical data (like favourite colours), you are using the wrong diagram entirely.
• Wrong belief: 'A frequency polygon and an ogive are both curves drawn on a histogram, so they show the same thing.' Correction: A frequency polygon connects the midpoints of each bar at their individual frequencies — it can rise and fall, and it shows distribution shape. An ogive connects cumulative totals at the upper class boundaries — it always rises, and it helps you find the median or any percentile. They answer completely different questions.
• Wrong belief: 'A pie chart is the best way to show proportions, no matter how many categories there are.' Correction: Pie charts work well for five or six categories where slices are clearly visible. Once you have more than five or six categories, the slices become thin slivers that are impossible to compare or label. For many categories, a bar chart lets you rank and compare far more clearly — use a pie chart only when the number of parts is small and you want to highlight one dominant share.