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Line Graph Interpretation

Introduction

Line Graph Interpretation tests your ability to read trends and exact values from data plotted over a continuous axis (usually time). This pattern is common in aptitude tests because many business and data problems show trends (sales, profit, population) across months or years.

Typical tasks: read exact values, compute differences, percentage change, average rate of change, and identify trends (increasing, decreasing, steady).

Pattern: Line Graph Interpretation

Pattern

Key concept: Read numeric values from points, then use difference, percentage-change, average (mean) or rate formulas depending on the question.

Useful formulas:
Absolute change = New - Old
% change = (New - Old) ÷ Old × 100
Average rate (per period) = Total change ÷ Number of periods

Step-by-Step Example

Question

The line graph below shows yearly revenue (in ₹ lakhs) of Company Z from 2018 to 2023.
Find: (a) The absolute increase in revenue from 2019 to 2023, and (b) the percentage increase over the same period.

Solution

  1. Step 1: Read the values from the graph

    2019 = ₹95 lakhs, 2023 = ₹170 lakhs.

  2. Step 2: Compute absolute increase

    Increase = 170 - 95 = ₹75 lakhs.

  3. Step 3: Compute percentage increase

    % increase = (75 ÷ 95) × 100 ≈ 78.95%.

  4. Final Answer:

    (a) ₹75 lakhs, (b) ≈ 78.95%

  5. Quick Check:

    95 + 75 = 170; 75 ÷ 95 ≈ 0.789 → 78.9% ✅

Quick Variations

1. Read values at specific x (year/month) and compute difference or % change.

2. Find average yearly growth: (Final - Initial) ÷ Number of years.

3. Estimate slope between two points for rate comparison.

4. When intermediate values missing, interpolate visually or use nearest ticks.

Trick to Always Use

  • Step 1 → Always write down the exact read-off numbers before calculating.
  • Step 2 → Use absolute-change first, then percentage to avoid sign errors.
  • Step 3 → For trends, check at least three consecutive points to confirm direction.

Summary

Summary

  • Always read values carefully from plotted points.
  • Use formulas for absolute and percentage change.
  • Cross-check visually on the graph for correctness.
  • Verify results with a quick calculation.

Example to remember:
Increase = 170 - 95 = 75; % increase ≈ 78.95%

Practice

(1/5)
1.

The line graph below shows annual sales (in ₹ lakh) of a company from 2019 to 2023. Find the total sales in all five years.

easy
A. 300
B. 260
C. 240
D. 270

Solution

  1. Step 1: Note given sales

    Values: 40, 50, 60, 70, 80 (all in ₹ lakh).

  2. Step 2: Add the values

    Total = 40 + 50 + 60 + 70 + 80 = 300 (₹ lakh).

  3. Step 3: Match units to options

    Options are in ₹ lakh, so final total = 300.

  4. Final Answer:

    300 → Option A

  5. Quick Check:

    Re-check sum: (40+50)=90, (60+70)=130, 90+130+80 = 300 ✅

Hint: Add all yearly values directly; group pairs to reduce errors.
Common Mistakes: Forgetting to include one year or mixing units.
2.

The line graph shows revenue (in ₹ crore) of a company over 5 years. Find the percentage increase from 2020 to 2023.

easy
A. 40%
B. 45%
C. 50%
D. 60%

Solution

  1. Step 1: Identify old and new values

    Old (2020) = ₹120 crore; New (2023) = ₹180 crore.

  2. Step 2: Apply percentage change formula

    % increase = (New - Old) ÷ Old × 100.

  3. Step 3: Compute

    % increase = (180 - 120) ÷ 120 × 100 = 60 ÷ 120 × 100 = 50%.

  4. Final Answer:

    50% → Option C

  5. Quick Check:

    120 × 1.5 = 180, so increase is 50% ✅

Hint: Use (New-Old)/Old × 100 for percentage increase.
Common Mistakes: Using the new value as denominator or reversing values.
3.

The line graph shows the production (in tonnes) of a factory from 2018 to 2022. Find the average production.

easy
A. 110
B. 108
C. 112
D. 114

Solution

  1. Step 1: Sum all productions

    80 + 100 + 120 + 100 + 140 = 540 (tonnes).

  2. Step 2: Divide by number of years

    Average = 540 ÷ 5 = 108.

  3. Step 3: Match to options

    108 → Option B.

  4. Final Answer:

    108 tonnes → Option B

  5. Quick Check:

    108 × 5 = 540 ✅

Hint: Average = (sum of values) ÷ (number of periods).
Common Mistakes: Dividing by wrong number of years or misadding values.
4.

The line graph below shows monthly electricity consumption (in units) from Jan to May. Find the month with the highest consumption.

medium
A. Jan
B. Feb
C. Apr
D. May

Solution

  1. Step 1: Read the plotted values

    Values are Jan=60, Feb=80, Mar=40, Apr=100, May=120.

  2. Step 2: Identify the maximum

    The highest value is 120 (May).

  3. Final Answer:

    May → Option D

  4. Quick Check:

    No month has value >120, so May is correct ✅

Hint: Find the highest plotted point or the largest numeric value.
Common Mistakes: Reading the lowest peak by mistake or misreading axis labels.
5.

The line graph shows profits (in ₹ crore) for a firm. Find the average annual increase between 2018 and 2022.

medium
A. 6.25
B. 5.5
C. 7.25
D. 6.5

Solution

  1. Step 1: Identify first and last values

    First (2018) = 25; Last (2022) = 50.

  2. Step 2: Find total increase

    Total increase = 50 - 25 = 25.

  3. Step 3: Divide by intervals (years - 1)

    Number of intervals = 4 → Average annual increase = 25 ÷ 4 = 6.25.

  4. Final Answer:

    6.25 crore per year → Option A

  5. Quick Check:

    6.25 × 4 = 25 ✅

Hint: Average increase = (Last - First) ÷ (number of intervals).
Common Mistakes: Dividing by total years instead of intervals (years - 1).

Mock Test

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