Data Interpretation & DI Formulae

Data Interpretation (DI) data को analyse करके meaningful conclusions निकालने की process है।

Key Skills in DI:

• Reading tables and charts
• Understanding units and scales
• Basic arithmetic operations
• Percentage calculations
• Ratio and proportion
• Average and weighted average
• Comparative analysis
• Estimation and approximation

Percentage किसी number को 100 के आधार पर व्यक्त करने का तरीका है।

Key Points:

• Percentage = "per cent" = "per hundred" (प्रति सौ)
• 100% = Whole
• 50% = Half (1/2)
• 25% = Quarter (1/4)
• 10% = One-tenth (1/10)

Examples:

• 25% of 200 = (25/100) × 200 = 50
• 15% of 300 = (15/100) × 300 = 45
• What % is 30 of 150? = (30/150) × 100 = 20%

• X% of Y: (X/100) × Y
• What % is X of Y: (X/Y) × 100
• Value after X% increase: Original × (100 + X)/100
• Value after X% decrease: Original × (100 − X)/100
• Original before X% increase: New × 100/(100 + X)
• Original before X% decrease: New × 100/(100 − X)

Example 1: What is 20% of 500? → (20/100) × 500 = 100

Example 2: 200 में 50 कितना प्रतिशत है? → (50/200) × 100 = 25%

• % Increase: (New − Original) / Original × 100
• % Decrease: (Original − New) / Original × 100

Important: Always use Original Value as denominator.

Example: Price increases from 200 to 250

• Change = 50, Original = 200
• % Increase = (50/200) × 100 = 25%

Example 2: Price decreases from 250 to 200

• Change = 50, Original = 250
• % Decrease = (50/250) × 100 = 20%

Successive Percentage:

Example: 10% increase followed by 10% decrease = 10 + (−10) + (10×−10)/100 = −1%

Ratio दो quantities के बीच के relationship को दर्शाता है।

Key Points:

• Ratio has no units
• Can be simplified (divide by HCF)
• Order matters (a:b ≠ b:a)

Share from Ratio:

• If ratio = a:b, total parts = a+b
• Share of a = (a/(a+b)) × Total
• Share of b = (b/(a+b)) × Total

Example: Total = 500, Ratio = 2:3

• Total parts = 5
• A = (2/5) × 500 = 200
• B = (3/5) × 500 = 300

Average numbers के set का central value है।

Key Formulae:

• Sum: Average × Number of items
• Number of items: Sum / Average
• Average of first n natural numbers: (n+1)/2
• Average of first n even numbers: (n+1)
• Average of first n odd numbers: n

Example: Find average of 5, 10, 15, 20, 25

• Sum = 75, Number = 5
• Average = 75/5 = 15

Weighted Average तब use होता है जब different items के अलग-अलग weights (importance) होते हैं।

Where w = weight, x = value

Example: Class has 20 boys with avg marks 70 and 30 girls with avg marks 80

• Σ(w×x) = (20×70) + (30×80) = 1400 + 2400 = 3800
• Σw = 20 + 30 = 50
• Weighted Average = 3800/50 = 76

Use in DI:

• Overall percentage when groups have different sizes
• Combined average of multiple groups
• CGPA/SGPA calculation

• Absolute Change: New − Original
• Percentage Change: (Absolute Change / Original) × 100
• Relative Change: New/Old (ratio)

Successive Percentage Change:

Example 1: 10% increase followed by 20% increase

• Net = 10 + 20 + (10×20)/100 = 30 + 2 = 32%

Example 2: 10% increase followed by 10% decrease

• Net = 10 + (−10) + (10×−10)/100 = 0 − 1 = −1%

• Absolute Comparison: Direct difference between values
• Relative Comparison: Ratio or percentage of values
• Ranking: Highest, lowest, second highest
• Trend Analysis: Increase/decrease over time
• Share Analysis: Contribution to total

Common Questions:

• "Which is highest/lowest?"
• "How much more/less than?"
• "What is the ratio of X to Y?"
• "What is the percentage contribution?"
• "What is the growth rate?"

• Step 1: Read the Title: Understand what the data is about
• Step 2: Check Units: Actual numbers, percentages, thousands, lakhs, crores
• Step 3: Observe Base Value: What total are percentages based on?
• Step 4: Identify Required Operation: Difference, ratio, average, percentage, trend
• Step 5: Estimate Before Calculation: Use approximation for quick answers
• Step 6: Recheck Denominator: Most common error in percentage questions

• Percentage: (Part/Whole) × 100
• Percentage Change: (New−Old)/Old × 100
• Net % Change: A + B + (A×B)/100
• Ratio: a:b = a/b
• Share from Ratio: (a/(a+b)) × Total
• Average: Sum/n
• Weighted Average: Σ(w×x)/Σw
• X% of Y: (X/100) × Y
• Value after X% increase: Original × (100+X)/100
• Value after X% decrease: Original × (100−X)/100

• Trap 1: Percentage increase and decrease of same percentage are not equal → 10% increase + 10% decrease = 1% net decrease
• Trap 2: Percentage change denominator = Original (not New)
• Trap 3: Average of percentages = direct average only if denominators are equal
• Trap 4: Higher absolute value ≠ higher percentage
• Trap 5: Ratio = actual numbers → Ratio is a relationship, not actual values
• Trap 6: Weighted average = simple average → Use weighted average when group sizes differ
• Trap 7: Successive discounts are not additive → 10% + 20% ≠ 30%

Table:

What is the total enrolment in 2024?

• A. 700
• B. 750
• C. 800
• D. 850

Explanation: 200+300+250 = 750.

What is the percentage increase in Course A from 2024 to 2025?

• A. 20%
• B. 25%
• C. 30%
• D. 40%

Explanation: (250−200)/200 × 100 = 25%.

What is the ratio of Course B to Course C in 2025?

• A. 5:6
• B. 6:5
• C. 5:4
• D. 4:5

Explanation: 360:300 = 6:5.

What is the average enrolment in 2025?

• A. 300
• B. 303
• C. 305
• D. 310

Explanation: (250+360+300)/3 = 910/3 = 303.33 ≈ 303.

Course B's enrolment in 2025 is what percentage of total 2025 enrolment?

• A. 30%
• B. 35%
• C. 39.6%
• D. 42%

Explanation: Total 2025 = 250+360+300 = 910; 360/910 × 100 = 39.56% ≈ 39.6%.

Key Formulae:

• X% of Y = (X/100) × Y
• % Increase = (New−Old)/Old × 100
• % Decrease = (Old−New)/Old × 100
• Net % Change = A + B + (A×B)/100
• Share = (Ratio/Total Ratio) × Total
• Weighted Avg = Σ(w×x)/Σw

DI Strategy:

• Read → Identify Unit → Select Base → Calculate → Compare → Verify

Common Traps:

• % increase ≠ % decrease (different denominators)
• Average of percentages ≠ direct average (different bases)
• Successive discounts ≠ additive

Exam Formula:

UGC NET में Data Interpretation & DI Formulae के questions percentage, ratio, average, and comparative analysis पर based होते हैं।