Data can tell fascinating stories. In this chapter, we learn how to represent, read, and interpret data using various graphs and diagrams — bar graphs, histograms, pie charts, and line graphs. Choosing the right representation helps communicate data clearly.
Data and Its Types
Raw data is collected information before organisation. Data can be discrete (exact values, like number of students) or continuous (ranges, like heights).
Frequency is how often a value or class occurs. A frequency distribution table organises data into classes.
Bar Graphs: Bars of uniform width represent frequency. Suitable for discrete data. Bars do not touch.
Histograms: Similar to bar graphs but for continuous data; bars touch each other. The x-axis shows class intervals.
Pie Charts (Circle Graphs): The circle represents the whole. Each sector represents a fraction of the total. Central angle for a category = (frequency/total) × 360.
Line Graphs: Used to show change over time (continuous data). Points are plotted and joined by lines.
Grouped frequency tables and class intervals:
Class interval: a range of values (e.g., 10–20).
Class width: upper limit – lower limit.
Class mark (midpoint): (upper + lower)/2.
In a survey of 60 students, 15 prefer cricket, 25 prefer football, 20 prefer badminton. Find the central angle for football in a pie chart.
Angle = (25/60) × 360 = 150 degrees.
Construct a frequency table for: 23, 25, 22, 28, 23, 25, 26, 24, 22, 25.
22 → 2 times; 23 → 2 times; 24 → 1 time; 25 → 3 times; 26 → 1 time; 28 → 1 time. Total = 10.
From a histogram, if the class 30–40 has frequency 12 and total = 60, what fraction of data is in 30–40?
Fraction = 12/60 = 1/5.
A pie chart shows that 90 degrees represents Mathematics. Total students = 120. How many prefer Mathematics?
Number = (90/360) × 120 = 30 students.
Line graph shows temperatures: Mon=30, Tue=32, Wed=28, Thu=35, Fri=31. Which day has the highest temperature?
Thursday (35 degrees).
Heights of 40 students: 140–150 cm (8), 150–160 cm (16), 160–170 cm (12), 170–180 cm (4). Find the class with the highest frequency.
150–160 cm (frequency 16).
In a bar graph, bars for subjects show English=50, Math=80, Science=60, Hindi=40. Find the ratio of Math to Hindi.
Ratio = 80:40 = 2:1.
- Key formulas:
- Central angle in pie chart = (component value / total) × 360
- Class mark = (lower limit + upper limit) / 2
- Relative frequency = frequency / total frequency
Common mistakes
- In a histogram, leaving gaps between bars (should be touching for continuous data).
- Calculating pie chart angles using proportions but forgetting to multiply by 360.
- Reading histograms as bar graphs (the two have different rules).
Summary
Graphs and charts are powerful tools for presenting data visually. Bar graphs suit discrete data; histograms suit continuous data; pie charts show proportions; line graphs show trends over time. Always label axes and include a title.