Presentation of Data

The full picture

Imagine your teacher hands you a list of 40 students' test scores, all jumbled. Could you spot in five seconds who scored highest, or how many students failed? Probably not. But the moment you sort those scores into a frequency table — or draw a bar chart — the picture becomes clear. That transformation is exactly what this chapter is about. Presentation of Data means organising collected data into tables or diagrams so that patterns, comparisons, and conclusions become easy to see. The SCERT Kerala syllabus focuses on two main approaches: tabular presentation (arranging data into rows and columns) and diagrammatic presentation (turning data into visual pictures like bars, pies, and curves).

A frequency table is the starting point for almost everything. You sort raw values into class intervals (also called class limits), count how many values fall in each class, and record that count as frequency. For example, suppose you survey 30 households in your neighbourhood about monthly electricity bills. You might group them as ₹0–₹500, ₹500–₹1000, ₹1000–₹1500, and so on. Each group is a class interval; its width (here, ₹500) should be equal across all classes for easy comparison. A well-made table has a clear title, column headings with units, and a source note at the bottom. Tables are precise — you can read exact numbers — but they demand careful reading. That is where diagrams help.

Bar diagrams are the simplest visual. You draw vertical (or horizontal) bars whose height represents the frequency of each category. Bars are separated by gaps because bar diagrams are used for discrete data — data made up of separate, countable categories such as the number of students in each class, or the number of shops selling each product. A pie chart divides a circle into slices, where each slice's angle is proportional to that category's share of the total (angle = share × 360°). Pies are ideal for showing parts of a whole — for instance, what fraction of a school's budget goes to salaries versus infrastructure.

Histograms look like bar diagrams but they behave differently. In a histogram, bars must touch each other, because histograms show continuous data — data that can take any value within a range, like height, weight, or income. More importantly, it is the area of each bar (width × height) that represents frequency, not just the height alone. This matters whenever class intervals are unequal. A frequency polygon is drawn by plotting a point at the midpoint of each class interval at its frequency, connecting those points with straight lines, and then extending the line down to the x-axis at the midpoints of one imaginary class before the first class and one imaginary class after the last class. It gives you a line shape of the distribution and is especially useful for comparing two datasets on the same graph.

An ogive (pronounced oh-jive) is the cumulative frequency curve. Instead of plotting plain frequency, you add up all frequencies up to and including each class — this running total is called cumulative frequency. You then plot each cumulative frequency against the upper class boundary of that class, and join the points with a smooth curve. The ogive always climbs from left to right and flattens as it nears the total. Its most powerful use: you can read off the median directly — the value on the x-axis where cumulative frequency equals half the total. Ogives also help you find any percentile or quartile, making them a favourite in board exams.

Choosing the right diagram is a skill in itself. Use a bar diagram when comparing separate categories (districts, years, products). Use a pie chart when showing the share each category holds in a total. Use a histogram when the data is continuous and grouped into class intervals. Use a frequency polygon to reveal the overall shape of a distribution or to overlay two distributions. Use an ogive when you need medians, percentiles, or cumulative information. Picking the wrong diagram — say, a pie chart to show quarterly sales trends over time — gives a confusing picture and loses marks in exams.

An Indian example

Anjali runs a small textile shop in Thrissur. After Onam, she has a notebook full of daily sales figures — 45 days of numbers between ₹4,000 and ₹22,000, all in a scramble. Her father tells her to 'just look at the numbers', but she cannot see any pattern. So she groups the sales into classes: ₹4,000–₹8,000, ₹8,000–₹12,000, ₹12,000–₹16,000, ₹16,000–₹20,000, and ₹20,000–₹24,000. She counts how many days fall in each class and draws a histogram. Now it is obvious: the tallest bar sits at ₹8,000–₹12,000, meaning most days she earns in that range. She also draws an ogive and reads off that the median day's sales was about ₹11,200. With this information she plans her re-stocking: she orders enough fabric for ₹10,000-worth of sales on a typical day and keeps a buffer for the rare ₹20,000+ days she spotted at the upper end of the histogram.

Common misconceptions to watch for

• Many students say: 'Bar diagrams and histograms are basically the same — both use bars.' They are not. A bar diagram has gaps between bars and is used for discrete categories (days of the week, types of shops). A histogram has no gaps — bars touch — and is used for continuous data grouped into class intervals. The gap is not decorative; it signals whether the data is discrete or continuous.
• A common exam mistake is to plot individual class frequencies for an ogive, treating it like a line graph. An ogive plots cumulative frequencies (the running total: first-class frequency, then first + second, and so on) against the upper class boundaries, joined by a smooth curve. It will always start near zero and slope upward to the total. If your curve goes up and down, you have plotted ordinary frequencies, not cumulative ones.
• Students often think a pie chart is the most 'complete' or versatile diagram and use it for everything, including trends over time. A pie chart shows each category's share of a fixed total — it is perfect for 'what fraction of the school budget goes to each department?' but useless for showing how sales changed from Q1 to Q4. For time-based or sequential comparisons, a bar diagram or line graph is always the right choice.