Skip to content
← Business Mathematics and Basic Statistics

Business Mathematics and Basic Statistics · Class 12 Commerce

Ch 6Graphical Representation of Statistical Data — Class 12 Business Mathematics and Basic Statistics, concept-first.

A line graph is one of the simplest and most widely used ways of presenting data that changes over time — daily temperatures, monthly sales, yearly exports, and so on.

13

Q&A

6

Concepts

~6m

Unit weightage

Start learning — read this chapter →

Key concepts

Hover a concept to preview it and jump to its most relevant Q&A.

Line Graph

Imagine you are tracking the temperature outside your window every hour from 6 AM to 6 PM. At 6 AM it is 15°C, at 7 AM it is 17°C, at 8 AM it is 20°C, and so on.

Most relevant Q&A

Start with this concept →

Chapter contents

The NCERT structure, section by section. Open a section to see its questions, then read the concept-first solution.

1

Line Graph

A line graph is one of the simplest and most widely used ways of presenting data that changes over time — daily temperatures, monthly sales, yearly exports, and so on.

2

Bar Diagram (Simple and Multiple Bar Diagrams)

A bar diagram represents categorical or discrete data using rectangular bars of equal width, drawn either vertically or horizontally, with the length (or height) of each bar proportional to the value…

3

Pie Diagram

A pie diagram (or pie chart) represents how a total is split among its components using a single circle divided into sectors, where each sector's angle (and hence its area) is proportional to the shar…

4

Histogram

A histogram represents a continuous (grouped) frequency distribution using a set of adjacent rectangles — one per class interval — drawn with no gaps between them, since the classes themselves are con…

5

Frequency Polygon

A frequency polygon is a line-graph representation of a grouped frequency distribution: instead of rectangles, the midpoint (class mark) of each class is plotted against its frequency, and consecutive…

6

Ogives (Cumulative Frequency Curves)

An ogive (pronounced 'oh-jive') is a graph of a cumulative frequency distribution — it shows, at a glance, how many observations lie below (or above) any given value, rather than how many observations…

7

Comparison of Statistical Data via Graphical Presentation

Graphs are not only a way of presenting a single data set clearly — they are one of the most effective ways of comparing two or more data sets at a glance, without a reader having to mentally process…

Exercises

+Show 6 questions6 questions
  1. Q8The rainfall (in mm) recorded in a city over six months is given below. Draw a line graph to represent this data, and state in which month t…Free
  2. Q9The number of cars sold by a dealer over five years is given below. Draw a simple bar diagram to represent this data, and find (a) the year…Free
  3. Q10The runs scored by two batsmen, Player X and Player Y, in five matches are given below. Draw a multiple bar diagram to compare them, and sta…Preview
  4. Q11A company's total annual expenditure of ₹20,00,000 is distributed under the following heads. Draw a pie diagram showing the percentage and a…Preview
  5. Q12The weekly wages (in ₹ hundred) of 45 workers are grouped as follows. Draw a histogram for this distribution, and superimpose its frequency…Preview
  6. Q13The marks obtained by 50 students in a test are grouped as follows. Draw the less-than ogive for this distribution and use it to estimate th…Preview

More questions

+Show 7 questions7 questions
  1. Example 1The monthly sales (in ₹ thousand) of a small shop for six months are given below. Draw a line graph to represent this data, and state in whi…Free
  2. Example 2The annual production (in units) of a small factory over five years is given below. Draw a simple bar diagram to represent this data, and id…Free
  3. Example 3The sales (in ₹ lakh) of two branches of a company over four years are given below. Draw a multiple bar diagram to compare the two branches,…Free
  4. Example 4A family's monthly budget of ₹16,000 is allocated as follows. Draw a pie diagram to represent this data, showing the angle of each sector. |…Preview
  5. Example 5The marks obtained (out of 50) by 50 students in a test are grouped as follows. Draw a histogram to represent this distribution. | Marks | 0…Preview
  6. Example 6Using the same marks distribution as Worked Example 5 (50 students, classes 0–10 to 40–50 with frequencies 4, 10, 16, 12, 8), draw the frequ…Preview
  7. Example 7The marks obtained by 60 students in an examination are grouped as follows. Draw the less-than ogive for this distribution, and use it to es…Preview