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Missing Data / Logical DI

Introduction

InMissing Data / Logical Data Interpretation (DI) problems-ல், table, chart, அல்லது paragraph-இல் சில values திட்டமிட்டு விடப்பட்டிருக்கும். கொடுக்கப்பட்ட totals, ratios, averages அல்லது relationships-ஐ பயன்படுத்தி, அந்த missing entries-ஐ logic-ஆக deduce செய்ய வேண்டும். இந்த pattern careful reasoning மற்றும் algebraic setup-ஐ பயிற்றுவிக்கிறது - dataset-இன் சில பகுதிகள் மறைக்கப்படும் exam-style DI-க்கு அவசியமான skills.

Pattern: Missing Data / Logical DI

Pattern

Key concept: totals, differences, ratios அல்லது averages-ஐ பயன்படுத்தி equations அமைத்து missing values-ஐ மீட்டெடுக்கவும்.

Typical approaches:

  1. கொடுக்கப்பட்ட table/paragraph-ஐ unknowns-க்கு variables-ஆக மாற்றவும்.
  2. Totals, row/column sums, averages அல்லது ratio relationships-இலிருந்து equations எழுதவும்.
  3. System-ஐ step-by-step-ஆக solve செய்யவும் (substitute அல்லது eliminate) மற்றும் units-ஐ check செய்யவும்.
  4. Consistency உறுதி செய்ய இறுதியில் sum அல்லது average check எப்போதும் செய்யவும்.

Step-by-Step Example

Question

கீழே உள்ள table-ல் Products P மற்றும் Q-ன் quarterly sales (₹ lakh-ல்) காட்டப்பட்டுள்ளது. ஒரு cell missing ஆக உள்ளது.

QuarterProduct PProduct QTotal (P+Q)
Q1403070
Q255-110
Q36045105
Q4455095

Find: Q2-ல் Product Q-க்கு missing value-ஐ கண்டுபிடிக்கவும்.

Solution

  1. Step 1: Knowns மற்றும் unknown-ஐ அடையாளம் காண்க:

    Q2-ல்: Product P = 55 (₹ lakh), Product Q = unknown (x), Total (P+Q) = 110.

  2. Step 2: Total-இலிருந்து equation அமைக்கவும்:

    P + Q = 110 → 55 + x = 110.

  3. Step 3: x-ஐ solve செய்யவும்:

    x = 110 - 55 = ₹55 lakh.

  4. Final Answer:

    ₹55 lakh (Q2-ல் Product Q).

  5. Quick Check:

    Q2 total = 55 + 55 = 110 ✅. மேலும் context-இல் அனைத்து totals-ும் சரியாக உள்ளதா என்பதை verify செய்யவும்.

Quick Variations

1. Row totals மற்றும் பிற columns தெரிந்திருக்கும்போது missing column sum - grand total-இலிருந்து known column sums-ஐ subtract செய்யவும்.

2. Missing average அல்லது count - Average = Total ÷ Count பயன்படுத்தி missing variable equation அமைக்கவும்.

3. சில cells missing ஆனால் row/column ratios கொடுக்கப்பட்டிருந்தால் - ratios-ஐ parts-ஆக மாற்றி variables assign செய்து simultaneous equations solve செய்யவும்.

Trick to Always Use

  • Step 1 → ஒவ்வொரு missing value-க்கும் variable (x, y, z) assign செய்து, extract செய்யக்கூடிய எல்லா equations-ஐ (row sums, column sums, ratios, averages) எழுதுங்கள்.
  • Step 2 → Substitution/elimination பயன்படுத்தி, சாத்தியமான இடங்களில் single-variable equation-ஆக reduce செய்யுங்கள்.
  • Step 3 → Solve செய்த பிறகு, original table-இல் values-ஐ substitute செய்து முழு sum/average check செய்து arithmetic slip இல்லையா உறுதி செய்யுங்கள்.

Summary

Summary

Missing Data / Logical DI problems-ல்:

  • Unknown cells-ஐ உடனே variables-ஆக மாற்றுங்கள்.
  • Totals, averages, அல்லது ratio relationships-இலிருந்து equations derive செய்யுங்கள்.
  • Systematic-ஆக solve செய்யுங்கள் (substitute/eliminate) - guessing தவிர்க்கவும்.
  • இறுதியில் consistency check (row/column sums, average, அல்லது total) எப்போதும் செய்யுங்கள்.

Practice

(1/5)
1.

Quarterly Sales Report (Missing Entry)

The table shows quarterly sales (in ₹ lakh) for Products A and B. One entry is missing. Use the given totals to find the missing data.

QuarterProduct AProduct BTotal (A + B)
Q1354580
Q240-85
Q35060110
Q4454085

Find the missing value for Product B in Q2.

easy
A. ₹45 lakh
B. ₹40 lakh
C. ₹50 lakh
D. ₹55 lakh

Solution

  1. Step 1: Identify knowns:

    Q2 total = 85; Product A in Q2 = 40.

  2. Step 2: Use total formula:

    Product A + Product B = Total → 40 + B = 85.

  3. Step 3: Solve:

    B = 85 - 40 = .

  4. Final Answer:

    ₹45 lakh → Option A.

  5. Quick Check:

    40 + 45 = 85 ✅

Hint: Subtract the known product value from the total to get the missing one.
Common Mistakes: Adding instead of subtracting when solving for the missing value.
2.

Employee Distribution (One Department Missing)

A company's workforce is divided into three departments: HR, Sales, and Tech. The table shows headcounts, but one value is missing.

DepartmentEmployees
HR40
Sales-
Tech100
Total180

Find the number of employees in Sales.

easy
A. 40
B. 35
C. 50
D. 60

Solution

  1. Step 1: Build equation from total:

    HR + Sales + Tech = Total → 40 + Sales + 100 = 180.

  2. Step 2: Solve for Sales:

    Sales = 180 - (40 + 100) = 180 - 140 = .

  3. Final Answer:

    40 → Option A.

  4. Quick Check:

    40 + 40 + 100 = 180 ✅

Hint: Subtract the sum of known department counts from the total to get the missing department.
Common Mistakes: Forgetting to include all known departments when subtracting from the total.
3.

College Attendance Data (Missing Average)

A college recorded monthly average attendance (in %) for four months. The overall average attendance for all months was 75%. Three months' data are known as shown below.

MonthAttendance %
January70
February80
March-
April75

Find the missing March attendance percentage.

easy
A. 72%
B. 75%
C. 74%
D. 78%

Solution

  1. Step 1: Use average formula:

    (January + February + March + April) ÷ 4 = 75 → (70 + 80 + x + 75) ÷ 4 = 75.

  2. Step 2: Solve for x:

    70 + 80 + x + 75 = 300 → 225 + x = 300 → x = 75.

  3. Final Answer:

    → Option B.

  4. Quick Check:

    (70 + 80 + 75 + 75) ÷ 4 = 300 ÷ 4 = 75 ✅

Hint: Multiply the overall average by the count to get the total, then subtract known months.
Common Mistakes: Forgetting to multiply average by the number of months before subtracting known values.
4.

Production Summary (Missing Yearly Output)

A factory’s total 3-year production was 7,200 units. The table shows production for 2021 and 2022. Find missing 2023 production.

YearProduction (units)
20212,100
20222,300
2023-
Total7,200

Find the production in 2023.

medium
A. 2,700
B. 2,800
C. 2,900
D. 3,000

Solution

  1. Step 1: Sum known years:

    2021 + 2022 = 2,100 + 2,300 = 4,400 units.

  2. Step 2: Subtract from total:

    2023 = Total - (2021 + 2022) = 7,200 - 4,400 = units.

  3. Final Answer:

    2,800 → Option B.

  4. Quick Check:

    2,100 + 2,300 + 2,800 = 7,200 ✅

Hint: Use Total - Sum(known entries) to find the missing year's output.
Common Mistakes: Adding totals instead of subtracting known values from the grand total.
5.

Regional Sales Distribution (Logic-Based Missing Value)

A company’s sales data (₹ lakh) for four regions are given below. The East region’s sales are equal to the average of North and South. The total for all regions is ₹500 lakh. Find the sales for the East region.

RegionSales (₹ lakh)
North120
South160
East-
West80
Total500
medium
A. 120
B. 150
C. 160
D. 140

Solution

  1. Step 1: Compute East from average rule:

    East = (North + South) ÷ 2 = (120 + 160) ÷ 2 = 280 ÷ 2 = .

  2. Step 2: Verify with total:

    Check sum: 120 + 160 + 140 + 80 = 500 → matches the given total, so East = 140 is consistent.

  3. Final Answer:

    140 → Option D.

  4. Quick Check:

    Average(120,160)=140 and total sum = 500 ✅

Hint: Compute the average first, then confirm that all region totals sum to the grand total.
Common Mistakes: Using the grand total without checking that the average condition is satisfied.

Mock Test

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