Data Interpretation - All Formulas & Shortcuts

Quick reference guide for DI with chart analysis and calculation shortcuts

📘 Basic Concepts

1. Types of Data Representation

Tables: Data in rows and columns Bar Charts: Vertical/horizontal bars Line Graphs: Trends over time Pie Charts: Percentage/proportion distribution Mixed Charts: Combination of above

⚡ Key Formulas

2. Percentage Calculations

Percentage of a value:

% = (Part/Total) × 100

Finding part from percentage:

Part = Total × (%/100)

Percentage increase:

% Increase = [(New - Old)/Old] × 100

Percentage decrease:

% Decrease = [(Old - New)/Old] × 100

3. Ratio & Proportion

Ratio from values:

A:B = Value_A : Value_B Simplify by dividing by HCF

Finding values from ratio:

If A:B = x:y and total = T A = T × x/(x+y) B = T × y/(x+y)

4. Average Calculations

Simple average:

Average = Sum of values / Number of values

Weighted average:

Avg = (n₁v₁ + n₂v₂ + … ) / (n₁ + n₂ + …)

🔥 Chart-Specific Shortcuts

5. Pie Chart Formulas

Value from angle:

Value = Total × (Angle/360)

Value from percentage:

Value = Total × (%/100)

Angle from percentage:

Angle = % × 3.6

Quick angles:

• 25% = 90°
• 50% = 180°
• 10% = 36°
• 33.33% = 120°

6. Bar Chart Analysis

Percentage of total:

% = (Bar Value/Sum of all bars) × 100

Ratio of two bars:

A:B = Height_A : Height_B

Growth rate:

Growth% = [(Year₂ - Year₁)/Year₁] × 100

7. Line Graph Formulas

Rate of change (slope):

Rate = (y₂ - y₁)/(x₂ - x₁)

Percentage change:

% Change = [(Value₂ - Value₁)/Value₁] × 100

Average change per period:

Avg Change = Total Change / Number of periods

💡 Quick Calculation Tricks

8. Percentage Shortcuts

10% of N: N/10 20% of N: N/5 25% of N: N/4 50% of N: N/2 33⅓% of N: N/3

Example: 25% of 840

= 840/4 = 210

9. Fraction to Percentage

Common conversions:

1/2 = 50% 1/3 = 33.33% 1/4 = 25% 1/5 = 20% 1/8 = 12.5% 2/3 = 66.67% 3/4 = 75% 4/5 = 80%

10. Approximation Techniques

Round to nearest 10:

472 ≈ 470 835 ≈ 840

Round to nearest 100:

1,847 ≈ 1,800 3,234 ≈ 3,200

For division, round both:

4,789/23 ≈ 4,800/24 = 200

🎯 Exam Patterns

Pattern 1: Percentage Contribution

Find X’s contribution to total:

Contribution% = (X/Total) × 100

Example: A=300, B=500, C=200, Total=1000

A% = 300/1000 × 100 = 30%

Pattern 2: Highest/Lowest

Compare values directly or as percentages

Quick comparison:

• Arrange in order
• Identify max/min
• Calculate difference if needed

Pattern 3: Year-on-Year Growth

Growth from Year 1 to Year 2:

Growth% = [(Y2 - Y1)/Y1] × 100

Cumulative growth over n years:

Total% = [(Final - Initial)/Initial] × 100

Pattern 4: Missing Data

Find missing value when total is given:

Missing = Total - Sum of known values

Find missing when ratio is given:

Use ratio to find missing value

📊 Table Analysis

11. Row/Column Operations

Row total:

Sum all values in row

Column total:

Sum all values in column

Row percentage:

% = (Cell Value/Row Total) × 100

Column percentage:

% = (Cell Value/Column Total) × 100

12. Comparison Formulas

Absolute difference:

Diff = |A - B|

Percentage difference:

% Diff = |(A - B)/B| × 100

Ratio comparison:

A/B compared to C/D Cross multiply: AD vs BC

💎 Advanced Shortcuts

13. Successive Percentage Change

Two changes of a% and b%:

Net% = a + b + (ab/100)

Example: +20% then -10%

Net = 20 + (-10) + (20×-10)/100 = 10 - 2 = 8% increase

14. Percentage of Percentage

x% of y% of N:

= (x × y × N)/10000

Example: 20% of 50% of 600

= (20 × 50 × 600)/10000 = 60

15. Break-even/Equal Point

When two values become equal:

Set up equation and solve

Example: A grows 10%, B grows 5%. When equal if A=100, B=110?

100(1.1)ⁿ = 110(1.05)ⁿ Solve for n

🔍 Speed Reading Tips

Tip 1: Scan for Extremes

Quickly identify:

• Maximum value
• Minimum value
• Largest change

Tip 2: Estimate Before Calculate

Rough estimate helps:

• Eliminate wrong options
• Verify final answer
• Save time

Tip 3: Use Given Data

Don’t assume:

• Use only given information
• Check units (thousands, lakhs, etc.)
• Note base year or reference

Tip 4: Question Pattern

Identify question type:

• Calculation (need exact value)
• Comparison (which is more/less)
• Trend (increasing/decreasing)
• Proportion (percentage/ratio)

🎓 Common Question Types

Type 1: Total/Sum Questions

Find total across years/categories:

Sum all relevant values

Type 2: Average Questions

Average of given values:

Average = Sum/Count

Type 3: Percentage Questions

X is what % of Y:

% = (X/Y) × 100

X is what % more/less than Y:

% more = [(X-Y)/Y] × 100 % less = [(Y-X)/Y] × 100

Type 4: Ratio Questions

Ratio of A to B:

A:B = Value_A : Value_B

A is how many times B:

Times = A/B

📝 Mental Math Techniques

Technique 1: Doubling/Halving

For multiplication:

35 × 16 = 35 × 2 × 8 = 70 × 8 = 560

Technique 2: Breaking Numbers

Split complex calculation:

47 × 25 = (40+7) × 25 = 1000 + 175 = 1175

Technique 3: Percentage Benchmarks

Use 10% as base:

10% of 480 = 48 20% = 96 30% = 144 25% = 120 (half of 50%)

🔗 Related Resources

Practice Questions:

• Data Interpretation Practice

Theory:

• DI Theory & Concepts

Related Topics:

• Percentage
• Ratio & Proportion
• Average

Study Resources:

• All-in-One Formula Sheet

Master percentage shortcuts - solve DI 3x faster! ⚡

Practice reading charts quickly - speed wins! 🚀