Presentation of Data
After collecting and organising data, the next step is presenting it in a form that is easy to understand and visually appealing. Good presentation reveals patterns, trends, and comparisons at a glance.
Forms of Data Presentation
1. Textual Presentation: Data is described in paragraph form. Suitable for a small amount of data. Easy to write but difficult to compare.
2. Tabular Presentation (Tables): Data arranged in rows and columns. More systematic and allows quick comparison. A well-constructed table has a title, row and column headings, units, source note, and footnotes.
3. Diagrammatic and Graphic Presentation: Data shown through diagrams or graphs. Most visually effective.
Types of Diagrams
- Bar Diagrams:
- Simple bar diagram: Single bars represent one variable.
- Multiple bar diagram: Two or more bars side by side for comparison.
- Sub-divided (component) bar diagram: Bars divided into segments showing components.
- Percentage bar diagram: Each bar totals 100%; segments show percentage share.
Pie Chart (Pie Diagram): A circle divided into sectors proportional to the values. Angle for each component = (Component value / Total) × 360 degrees.
Frequency Histogram: A bar graph with no gaps between bars, drawn for frequency distributions. X-axis: class intervals; Y-axis: frequency (or frequency density for unequal widths).
Frequency Polygon: A line graph connecting midpoints of the tops of histogram bars. Useful for comparing two or more distributions. Extend to the midpoints of the class before the first and after the last.
- Ogive (Cumulative Frequency Curve):
- Less-than ogive: Plot cumulative frequency against upper class limits; curve rises from left to right.
- More-than ogive: Plot cumulative frequency against lower class limits; curve falls from left to right.
- The x-value at the intersection of both ogives gives the Median.
Arithmetic Line Graph (Time Series Graph)
Used to show changes in a variable over time. Time is plotted on the x-axis and the variable on the y-axis. Effective for showing trends.
Worked Examples
Calculate the angle for the 'Agriculture' sector if it contributes Rs 30 lakh out of a total GDP of Rs 120 lakh.
Angle = (30 / 120) × 360 = 0.25 × 360 = 90 degrees
Draw a frequency polygon. Given classes 0-10, 10-20, 20-30 with frequencies 5, 8, 4. What are the midpoints?
Midpoints: 5, 15, 25. Plot (5, 5), (15, 8), (25, 4). Extend to (-5, 0) and (35, 0).
Why is there no gap between bars in a histogram but there are gaps in a bar diagram?
Histogram represents a continuous frequency distribution — class intervals are continuous with no breaks. Bar diagrams represent discrete or categorical data where gaps signify separateness of categories.
The exports of India were: 2018 — Rs 23 lakh crore, 2019 — Rs 26 lakh crore, 2020 — Rs 21 lakh crore. Which diagram is best?
An arithmetic line graph (time series graph) is best to show changes in exports over time.
A percentage bar diagram shows that 60% of income is spent on food, 20% on rent, and 20% on others. If total income = Rs 10,000, find the amount on food.
60% of Rs 10,000 = Rs 6,000 on food.
From an ogive, a student finds the median at x = 45. Verify: if 50% of students scored below 45 in a class of 60, cumulative frequency at 45 should be?
50% of 60 = 30. If the less-than ogive shows cumulative frequency 30 at the value 45, the median is confirmed as 45.
A sub-divided bar diagram shows total sales of two products A and B as Rs 80,000 and Rs 60,000. Product A has components: domestic Rs 50,000 and export Rs 30,000. Draw the first bar.
First bar height = Rs 80,000. Lower segment = Rs 50,000 (domestic), upper segment = Rs 30,000 (export), stacked together.
Common mistakes
Common mistakes
Students confuse histogram with bar diagram. Remember — histogram has NO gaps (continuous data); bar diagrams DO have gaps (discrete/categorical data). Also, in a pie chart, always verify all angles sum to 360 degrees.
Summary
Data can be presented textually, in tables, or through diagrams/graphs. Key diagrams include bar diagrams, pie charts, histograms, frequency polygons, ogives, and time series graphs. Each is suited for specific types of data. Ogives can be used to determine the median graphically.