Skip to content

Fundamentals of Business Mathematics and Statistics · Statistical Representation of Data

Diagrammatic Representation of Data: Bar Diagrams and Pie Charts

Updated 10 October 2026 · Fact-checked

Diagrammatic representation shows data as bars, circles or other shapes so you can compare values at a glance. Bar diagrams compare values by length. Pie charts show shares of a total, with each angle = (value ÷ total) × 360°. In MCQs, identify the diagram type, then apply its rule.

Understand Diagrammatic Representation of Data

A diagram is a picture of data. Instead of reading a table of numbers, you look at bars or circles and see which value is bigger, which is growing and how the parts fit into the whole. Diagrams are easy to read and remember, but they show approximate values, not exact ones.

One-dimensional diagrams use only length or height. The width of a bar is the same for all bars and carries no meaning. The main types are:

  • Simple bar diagram: one bar per item, for one set of data, such as a firm's yearly sales.
  • Multiple bar diagram: bars for two or more related series placed side by side for each period, such as sales and profit for each year. Different shading tells the series apart.
  • Component (sub-divided) bar diagram: each bar is split into parts that add up to the total, such as total cost split into material, labour and overheads.
  • Percentage bar diagram: a component bar where every bar is scaled to 100%, so each part shows its percentage share. Use it to compare structure, not totals.

Two-dimensional diagrams use area. Rectangles, squares and circles are the usual ones. Here the area, not the length, represents the value. So if one value is 4 times another, the side of a square is only 2 times (square root of 4) and the radius of a circle is also 2 times.

A pie chart (angular diagram) is a circle divided into sectors. The full circle is 360° and stands for the total. Each sector's angle is proportional to its component. A pie chart shows shares of one total at one point in time. It cannot show change over time well.

Other diagrams include pictograms (small pictures, each standing for a fixed quantity) and cartograms (data shown on a map). In the exam, you mostly need to know which diagram suits which data, and to do simple angle and percentage calculations.

Key formulas to remember

Pie chart angle
Angle of a component = (Component value ÷ Total) × 360°
All angles must add up to 360°.
Angle from percentage
Angle = (Percentage ÷ 100) × 360° = percentage × 3.6°
10% = 36°, 25% = 90°, 50% = 180°.
Percentage bar height
Component percentage = (Component ÷ Bar total) × 100
Every bar in a percentage bar diagram has the same total height of 100%.
Scaling a two-dimensional diagram
Side of square ∝ √value; Radius of circle ∝ √value
Area is proportional to the value, so lengths scale by the square root.
Choosing the diagram
Compare values: simple or multiple bar. Parts of a total: component bar or pie. Share structure across bars: percentage bar.
Use this to answer 'which diagram is suitable' questions.

How to solve Diagrammatic Representation of Data questions

Use this method for any MCQ on diagrams, whether it asks for a definition, a choice of diagram or a calculation.

  1. 1Read the question and identify whether it asks about a type of diagram, a calculation or a reading from a diagram.
  2. 2Look at the data: one series, two or more series, or parts of a total. This decides the diagram type.
  3. 3For a pie chart, find the total first. Then compute each angle as (value ÷ total) × 360°.
  4. 4Check that your angles add up to 360°, or the percentages add up to 100%.
  5. 5For a two-dimensional diagram, remember that area stands for value, so take square roots to compare sides or radii.
  6. 6For a percentage bar diagram, convert each component into a percentage of its own bar total.
  7. 7Match your answer to the four options and eliminate options that break a basic rule, such as angles over 360°.

Quickest way: Shortcut for pie chart angles and diagram choice

When to use it: Use it when the total divides neatly into 360 or when the question only asks which diagram fits.

  1. If the total is 360 or divides 360 easily, work out 360 ÷ total once. Then multiply each value by it.
  2. Example: total ₹120 gives 360 ÷ 120 = 3°, so every ₹1 equals 3°.
  3. Remember the common angles: 25% = 90°, 10% = 36°, 5% = 18°, 1% = 3.6°.
  4. For choosing diagrams, use keywords: 'side by side' means multiple bar, 'split into parts' means component bar, 'shares in %' means percentage bar or pie.
  5. If one option is a bar chart for a total split into shares, check whether a pie chart is also an option and pick the one the question names.

Common mistakes in Diagrammatic Representation of Data

  • Mixing up a multiple bar diagram and a component bar diagram.

    Both show more than one figure per period, so they look similar.

    Fix: In a multiple bar diagram, the bars stand side by side and each is a separate series. In a component bar, one bar is stacked into parts that add to the total.

  • Using 100 instead of 360 in a pie chart angle.

    Students think of percentages and forget that a circle has 360 degrees.

    Fix: Always write angle = (value ÷ total) × 360°. If you have a percentage, multiply by 3.6.

  • Thinking the width of a bar matters.

    A wider bar looks bigger, so students assume it carries meaning.

    Fix: In one-dimensional diagrams only the length or height shows the value. Widths are kept equal.

  • Comparing two-dimensional diagrams by simple ratio of sides.

    Students forget that area represents the value.

    Fix: If one value is 9 times another, the side of a square is 3 times, not 9 times. Take the square root.

  • Using a percentage bar diagram to compare actual totals.

    All bars look equal in height, and students forget why.

    Fix: Percentage bars show only the structure or share of each part. For actual totals, use a component bar diagram.

  • Not checking that the angles add up to 360°.

    Students rush and skip the final check.

    Fix: Add the angles at the end. A quick sum catches most arithmetic slips.

Worked examples

Example 1

A company's monthly expenditure of ₹36,000 is: rent ₹9,000, salaries ₹15,000, raw material ₹8,000 and others ₹4,000. In a pie chart, what is the angle for salaries?

Show the solution
  1. Total expenditure = 9,000 + 15,000 + 8,000 + 4,000 = ₹36,000.
  2. Angle for salaries = (15,000 ÷ 36,000) × 360°.
  3. 360 ÷ 36,000 = 0.01°, so each rupee stands for 0.01°.
  4. Angle = 15,000 × 0.01 = 150°.
  5. Check: rent 90°, salaries 150°, raw material 80°, others 40°. Sum = 360°.

Answer: 150°

Example 2

The areas of two squares drawn to show the sales of two firms are in the ratio of their sales. If the sales are ₹16 crore and ₹64 crore, what is the ratio of the sides of the two squares?

Show the solution
  1. In a two-dimensional diagram, area is proportional to the value.
  2. Ratio of areas = 16 : 64 = 1 : 4.
  3. Side is the square root of area, so ratio of sides = √1 : √4.
  4. Ratio of sides = 1 : 2.

Answer: 1 : 2

Exam tips

  • Questions on this topic are mostly short and definition-based. Learn the four bar diagram types by one-line distinctions.
  • For pie chart angle questions, compute only the angle asked. Do not draw or calculate every sector.
  • If a question says 'area' or 'circle radius', think square root immediately.
  • When two options look alike (multiple bar and component bar), read the data description: separate series or parts of one total.
  • There is no negative marking, so attempt every question. Eliminate options that break a rule first, then guess.

Practice questions from Statistical Representation of Data

Diagrammatic Representation of Data in other exams

The same ground in other exams, if you are preparing for more than one or want another angle on it.

Diagrammatic Representation of Data: frequently asked questions

What is the difference between a simple bar diagram and a multiple bar diagram?

A simple bar diagram shows one series of data, with one bar per item or period. A multiple bar diagram shows two or more related series side by side for each item or period. It lets you compare the series directly, such as sales and profit for each year.

How do you draw a pie chart in statistics?

Find the total of all components. Work out each angle as (value ÷ total) × 360°. Draw a circle, then mark the sectors one after another using a protractor. Label each sector and check that the angles add up to 360°.

What is a component bar diagram?

It is a bar that is divided into parts, where each part shows one component of the total. The full bar height equals the total. It is useful for showing how a total, such as cost, is made up of material, labour and overheads.

When should I use a percentage bar diagram?

Use it when you want to compare the structure or share of components across different bars, not the actual totals. Each bar is scaled to 100%, so the parts show percentages.