Quantitative Aptitude · Statistical Description of Data

Diagrammatic Presentation of Data: Bar Diagrams, Pie Charts and Pictograms

Updated 1 October 2026 · Fact-checked

Diagrammatic presentation shows data through shapes such as bars, circles and symbols instead of tables. Bar diagrams compare values by length, component bar charts split totals into parts, and pie charts show shares as angles. To solve questions, read the scale, then convert values to heights, percentages or angles.

Understand Diagrammatic Presentation of Data

A diagram is a picture of data. It lets a reader compare values at a glance. A table gives exact figures. A diagram gives a quick impression. That is why diagrams suit comparison and are weak for precise reading.

A simple bar diagram uses one bar per category. All bars have the same width and the same gap. Only the height (or length) carries the value. Bars start from a zero base line. If the base is not zero, the picture misleads.

A multiple bar diagram places two or more bars side by side for each category, for example sales and profit of each year. It compares related series. A component (sub-divided) bar diagram stacks the parts of a total in one bar, for example a year's cost split into labour, material and overhead. It shows the total and its parts together. A percentage component bar diagram makes every bar the same height (100%) so only the share of each part is compared.

A pie chart is a circle cut into sectors. The whole circle is 360° and stands for the total. Each sector's angle is proportional to its value. Pie charts show shares of one total at one point in time. They do not show trends well.

A pictogram uses small symbols, each standing for a fixed quantity, for example one car icon = 1,000 cars. Part of a symbol shows part of that quantity. Pictograms are easy to read but approximate.

Key formulas to remember

Angle of a sector in a pie chart: Angle = (Value of component ÷ Total) × 360°; All sector angles must add up to 360°.
Angle from percentage: Angle = (Percentage ÷ 100) × 360° = Percentage × 3.6°; 1% of the total equals 3.6°.
Value from angle: Value = (Angle ÷ 360°) × Total; Use when the chart gives angles and the total is known.
Percentage of a component in a component bar: Percentage = (Part ÷ Bar total) × 100; Used to convert a component bar into a percentage component bar.
Pictogram symbols: Number of symbols = Value ÷ Value per symbol; A half symbol means half the value per symbol.

How to solve Diagrammatic Presentation of Data questions

Use this method for any question on bar diagrams, pie charts or pictograms.

1Identify the diagram type: simple bar, multiple bar, component bar, pie chart or pictogram.
2Read the title, axis labels, units and scale (or the value per symbol). Note whether values are in thousands, lakhs or crores.
3Find what the question asks: a value, a share, a difference, a ratio, an angle or the best diagram to use.
4For a pie chart, convert between value, percentage and angle using the 360° rule.
5For a bar chart, read heights against the scale, then add, subtract or take ratios as required. In a component bar, remember the bar total is the sum of its parts.
6Check your answer: pie angles add to 360°, percentages add to 100%, and the unit matches the options.

Quickest way: Shortcut for diagram questions under time pressure

When to use it: Use it when the question gives a pie chart or bar chart and the options are numerically far apart.

Use 1% = 3.6° and simple fractions of the total: 90° is one quarter, 120° is one third, 60° is one sixth.
Compare angles directly when only ratios are asked. The ratio of values equals the ratio of angles, so you need no total.
Round bar readings to the nearest gridline and eliminate options that are clearly too large or too small.
If the question asks which diagram suits the data, match the purpose: compare categories means bar, parts of a total means pie or component bar, simple public display means pictogram.
Skip long chart-reading sets with many sub-parts if the scale is unclear. Come back if time remains, since a wrong answer costs 0.25 marks.

Common mistakes in Diagrammatic Presentation of Data

Using the wrong total when finding a pie chart angle.
Students divide by one of the parts or by a wrong subtotal instead of the grand total.
Fix: Add all components first. Then compute Angle = (Part ÷ Total) × 360° and check that all angles sum to 360°.
Confusing multiple bar and component bar diagrams.
Both use several pieces of data per category, so they look alike.
Fix: Multiple bars sit side by side and show separate series. Component bars stack parts that add to a total. Ask: do the pieces add up to a meaningful total?
Forgetting the unit or scale on the axis.
Students read the bar height and skip the label such as ₹ in lakhs or 'in thousands'.
Fix: Read the unit line before any calculation and write it beside your answer.
Treating a percentage component bar as showing actual values.
All bars have equal height, so students assume totals are equal.
Fix: A percentage component bar shows only shares. It cannot compare absolute amounts between bars.
Reading a pie chart's angle as a percentage.
Angle and percentage are both numbers on the chart, and students mix 360 and 100.
Fix: Divide the angle by 3.6 to get the percentage, or divide by 360 to get the fraction.
Counting a half symbol in a pictogram as a full one.
Students count symbols quickly without checking partial ones.
Fix: Count full symbols, add half symbols as half, then multiply by the value per symbol.

Worked examples

Example 1

A company's expenses total ₹7,20,000. Salaries are ₹2,40,000, raw material ₹3,00,000 and the rest is overheads. In a pie chart, what is the angle for raw material?
A) 120°
B) 150°
C) 90°
D) 144°

Show the solution

Total = ₹7,20,000 and raw material = ₹3,00,000.
Fraction = 3,00,000 ÷ 7,20,000 = 5/12.
Angle = 5/12 × 360° = 150°.

Answer: B) 150°

Example 2

A pie chart shows the spending of a family with monthly income ₹48,000. Food has a sector angle of 105°. How much is spent on food?
A) ₹12,000
B) ₹14,000
C) ₹16,000
D) ₹18,000

Show the solution

Value = (Angle ÷ 360°) × Total.
Food = 105/360 × 48,000.
105/360 = 7/24.
7/24 × 48,000 = 7 × 2,000 = ₹14,000.

Answer: B) ₹14,000

Example 3

In a pictogram, one symbol stands for 250 scooters. Sales in a month are shown as 6 full symbols and one half symbol. How many scooters were sold?
A) 1,500
B) 1,625
C) 1,750
D) 1,875

Show the solution

Full symbols: 6 × 250 = 1,500.
Half symbol = 250 ÷ 2 = 125.
Total = 1,500 + 125 = 1,625.

Answer: B) 1,625

Exam tips

Questions are usually either numerical (angles, values, shares) or conceptual (which diagram suits this data). Prepare both types.
Memorise the definitions: multiple bar compares separate series, component bar splits a total, pie shows shares of one whole.
Use simple fractions of 360° (one half = 180°, one third = 120°, one quarter = 90°) to avoid long division.
Check the unit and scale line before reading any bar, as options often differ only by a factor of 10 or 1,000.
Do not guess blindly on a chart question you cannot read. Eliminate options first, since each wrong answer loses 0.25 marks.

Practice questions from Statistical Description of Data

Diagrammatic Presentation of Data: frequently asked questions

What is the difference between a multiple bar chart and a component bar chart?

A multiple bar chart places separate bars side by side for each category to compare related series. A component bar chart stacks the parts of a total inside one bar. Use multiple bars to compare, and component bars to show composition.

How do I draw a pie chart in statistics?

Find the total of all components. Convert each component to an angle using (Value ÷ Total) × 360°. Draw a circle, mark the angles one after another from a starting radius, and label each sector. Check that the angles sum to 360°.

When should I use a pie chart instead of a bar diagram?

Use a pie chart when you want to show how one total divides into a few parts at one point in time. Use a bar diagram when you need to compare many categories or values over time. Pie charts become hard to read with too many sectors.

Is a pictogram accurate?

A pictogram is approximate. Each symbol stands for a fixed quantity, and part symbols show only rough fractions. It is good for quick public display and weak for exact values.