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Data Comparison Across Years / Categories

Introduction

कई Data Interpretation (DI) questions में different years या categories के values compare करने होते हैं ताकि growth, decline या relative performance पता चले। यह pattern इसलिए important है क्योंकि exams में अक्सर ranking, fastest growth, या year-on-year change निकालने वाले questions पूछे जाते हैं।

Pattern: Data Comparison Across Years / Categories

Pattern

Same base period पर absolute change और percentage change compare करके पता करें कि किसका growth सबसे तेज़ या सबसे धीमा है।

Key formulas:
Absolute change = New value - Old value
Percentage change = (New - Old) ÷ Old × 100

Step-by-Step Example

Question

नीचे दिया गया table चार cities की population (in thousands) 2019 और 2021 के लिए दिखाता है। 2019 से 2021 के बीच किस city का percentage growth सबसे ज़्यादा है?

City2019 (’000)2021 (’000)
Alpha120132
Beta90108
Gamma150165
Delta8096

Solution

  1. Step 1: हर city का absolute change निकालें

    Alpha: 132 - 120 = 12 (’000)
    Beta: 108 - 90 = 18 (’000)
    Gamma: 165 - 150 = 15 (’000)
    Delta: 96 - 80 = 16 (’000)

  2. Step 2: Percentage growth (2019 को base लेकर)

    Formula: (New - Old) ÷ Old × 100

    Alpha: (12 ÷ 120) × 100 = 10.00%
    Beta: (18 ÷ 90) × 100 = 20.00%
    Gamma: (15 ÷ 150) × 100 = 10.00%
    Delta: (16 ÷ 80) × 100 = 20.00%

  3. Step 3: Highest % growth identify करें

    Beta और Delta दोनों का percentage growth 20.00% है - यानी दोनों highest हैं।

  4. Final Answer:

    Beta और Delta (tie)

  5. Quick Check:

    Beta: (108 - 90) ÷ 90 = 18 ÷ 90 = 0.2 = 20% ✔️

Quick Variations

1. दो से ज़्यादा years compare करने हों तो CAGR या year-on-year % growth use करें।

2. Categories compare करने में भी यही formulas लागू होते हैं - base year वही रखें जो question में दिया हो।

3. अगर base values बहुत अलग हों, तो fair comparison के लिए percentage change use करें; absolute change सिर्फ raw difference बताता है।

Trick to Always Use

  • Step 1: Absolute change पहले निकालें - इससे biggest movers दिख जाते हैं।
  • Step 2: Percentage change = (New - Old) ÷ Old × 100 हमेशा correct base year पर apply करें।
  • Step 3: अगर percentage tie हो और question “largest increase” पूछे, तो absolute change compare करें।

Summary

Summary

In the Data Comparison Across Years / Categories pattern:

  • Absolute change = New - Old raw difference देता है।
  • Percentage change proportional growth दिखाता है।
  • Comparison हमेशा same base year पर ही करें।
  • Units (₹, %, ’000) match हों तभी compare करें।
  • एक entry का quick re-check हमेशा accuracy confirm करता है।

Practice

(1/5)
1.

School Enrollment - Compare 2018 vs 2020

The table shows student counts in three streams for 2018 and 2020. Which stream had the highest percentage growth from 2018 to 2020?

Stream2018 (students)2020 (students)
Arts1,2001,440
Science1,5001,650
Commerce800880
easy
A. Arts
B. Science
C. Commerce
D. All equal

Solution

  1. Step 1: Compute absolute increases (2020 - 2018):

    Arts: 1,440 - 1,200 = 240 students.
    Science: 1,650 - 1,500 = 150 students.
    Commerce: 880 - 800 = 80 students.

  2. Step 2: Compute percentage growth using 2018 as base:

    Arts: (240 ÷ 1,200) × 100 = 20.00%.
    Science: (150 ÷ 1,500) × 100 = 10.00%.
    Commerce: (80 ÷ 800) × 100 = 10.00%.

  3. Step 3: Compare percentages:

    Highest percentage growth = Arts (20.00%).

  4. Final Answer:

    Arts → Option A.

  5. Quick Check:

    240 ÷ 1,200 = 0.20 → 20% ✅

Hint: Compute absolute change first, then convert to % by dividing by the older year's value.
Common Mistakes: Comparing absolute increases directly instead of percentage when bases differ.
2.

Company Revenues - 2019 vs 2021 (₹ lakh)

The table shows revenues of three companies in 2019 and 2021. Which company had the largest absolute increase in revenue from 2019 to 2021?

Company2019 (₹ lakh)2021 (₹ lakh)
X400500
Y350420
Z300360
easy
A. X
B. Y
C. Z
D. Tie between X & Y

Solution

  1. Step 1: Compute absolute increases (2021 - 2019):

    X: 500 - 400 = 100 (₹ lakh).
    Y: 420 - 350 = 70 (₹ lakh).
    Z: 360 - 300 = 60 (₹ lakh).

  2. Step 2: Identify largest absolute increase:

    Largest increase = 100 (₹ lakh) for Company X.

  3. Final Answer:

    X → Option A.

  4. Quick Check:

    100 > 70 > 60 ✅

Hint: When asked 'largest absolute increase' use raw differences (new - old) rather than %.
Common Mistakes: Mixing up absolute increase with percentage increase.
3.

Product Sales - Yearly Totals (₹ lakh)

The table shows sales of four products across three years. Which year had the highest total sales?

Product2019 (₹ lakh)2020 (₹ lakh)2021 (₹ lakh)
A120140160
B150160170
C8090100
D90100120
easy
A. 2019
B. 2020
C. Cannot determine
D. 2021

Solution

  1. Step 1: Sum totals for each year:

    2019 total = 120 + 150 + 80 + 90 = 440 (₹ lakh).
    2020 total = 140 + 160 + 90 + 100 = 490 (₹ lakh).
    2021 total = 160 + 170 + 100 + 120 = 550 (₹ lakh).

  2. Step 2: Compare yearly totals:

    2019 = 440; 2020 = 490; 2021 = 550 → highest = 2021.

  3. Final Answer:

    2021 → Option D.

  4. Quick Check:

    550 > 490 > 440 ✅

Hint: When asked about 'which year had highest total', sum columns year-wise and compare.
Common Mistakes: Comparing product-wise instead of year-wise totals.
4.

Vehicle Sales by Region - 2017 vs 2019

The table shows vehicle sales (units) in four regions for 2017 and 2019. Which region had the highest percentage growth from 2017 to 2019?

Region2017 (units)2019 (units)
North1,5001,650
South1,2001,560
East900990
West800880
medium
A. North
B. South
C. East
D. West

Solution

  1. Step 1: Compute absolute increases (2019 - 2017):

    North: 1,650 - 1,500 = 150.
    South: 1,560 - 1,200 = 360.
    East: 990 - 900 = 90.
    West: 880 - 800 = 80.

  2. Step 2: Compute percentage growth using 2017 as base:

    North: (150 ÷ 1,500) × 100 = 10.00%.
    South: (360 ÷ 1,200) × 100 = 30.00%.
    East: (90 ÷ 900) × 100 = 10.00%.
    West: (80 ÷ 800) × 100 = 10.00%.

  3. Step 3: Compare percentages:

    Highest percentage growth = South (30.00%).

  4. Final Answer:

    South → Option B.

  5. Quick Check:

    360 ÷ 1,200 = 0.30 → 30% ✅

Hint: When region sizes differ, percentage compares fairly - compute (new - old) ÷ old × 100.
Common Mistakes: Picking the region with largest absolute increase ignoring base sizes.
5.

Company Expenses by Category - 2018 vs 2020 (₹ lakh)

The table shows expenses under categories for 2018 and 2020. Which category recorded the highest percentage increase from 2018 to 2020?

Category2018 (₹ lakh)2020 (₹ lakh)
Sales100130
Admin6066
R&D4064
Marketing5070
medium
A. Sales
B. Admin
C. R&D
D. Marketing

Solution

  1. Step 1: Compute absolute increases (2020 - 2018):

    Sales: 130 - 100 = 30.
    Admin: 66 - 60 = 6.
    R&D: 64 - 40 = 24.
    Marketing: 70 - 50 = 20 (all in ₹ lakh).

  2. Step 2: Compute percentage growth using 2018 as base:

    Sales: (30 ÷ 100) × 100 = 30.00%.
    Admin: (6 ÷ 60) × 100 = 10.00%.
    R&D: (24 ÷ 40) × 100 = 60.00%.
    Marketing: (20 ÷ 50) × 100 = 40.00%.

  3. Step 3: Compare percentages:

    Highest percentage increase = R&D (60.00%).

  4. Final Answer:

    R&D → Option C.

  5. Quick Check:

    24 ÷ 40 = 0.6 → 60% ✅

Hint: Smaller bases can produce larger % growth - always compute percent after finding absolute change.
Common Mistakes: Choosing the largest absolute increase without considering base size.

Mock Test

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