Data Interpretation: Notes और MCQ Practice

Simple Explanation (आसान भाषा में)\nData Interpretation में tables, graphs, charts से जल्दी‑जल्दी जानकारी निकालनी होती है। मुख्य बात है data को सही पढ़ना, जरूरी numbers चुनना और calculations systematic ढंग से करना। समय बचाने के लिए ratios और percentages के shortcuts याद रखें.\n\nImportant Formulas / Rules\n- Percentage change = (New − Old) ÷ Old × 100\n- Part‑wise % = Part ÷ Total × 100\n- Ratio → a:b = a ÷ (a+b) × 100% (for each part)\n- Average = Sum ÷ n\n- Simple Interest = P × R × T ÷ 100\n\nQuick Tricks\n1. Cross‑multiply: a:b = c:d → a×d = b×c, instantly दो unknowns find करो.\n2. Series average shortcut: अगर arithmetic series है, तो average = (first + last) ÷ 2, बिना सभी terms जोड़ें.\n\nCommon Mistakes\n- Units ignore करना: “kg” को “g” में बदलना या vice‑versa भूल जाना → answer wrong.\n- Rounding early: Approximation को बहुत पहले apply करना, जिससे final answer में noticeable error आ जाता है.

1. Concept

Data Interpretation (DI) is a section that tests your ability to analyse, interpret and draw conclusions from data presented in tables, charts, graphs, or mixed formats. The questions are usually based on a single data set and ask you to compute values, percentages, ratios, averages, growth rates, etc. Speed and accuracy are crucial because the data may be dense and the time limit is tight.

2. Important formulas / rules / facts

• Percentage change = (New - Old) ÷ Old × 100
• Average (Mean) = Sum of all values ÷ Number of values
• Ratio = A : B can be written as A ÷ B
• Proportion: If a/b = c/d then a×d = b×c
• Simple interest = P × R × T ÷ 100 (use only when explicitly given)
• Growth rate (annual) = ((Final ÷ Initial) ^ (1/Number of years) - 1) × 100
• Conversion of units: 1 km = 1000 m, 1 hr = 60 min, etc.
• Cumulative total: Add successive values; for decremental series subtract.
• Weighted average: (Σ (value × weight)) ÷ Σ weight

3. Solved Examples

Example 1

A company’s sales for the first four quarters are: Q1 – 120 units, Q2 – 150 units, Q3 – 130 units, Q4 – 200 units. What is the average quarterly sales?

Solution

1. Sum = 120 + 150 + 130 + 200 = 600 units
2. Number of quarters = 4
3. Average = 600 ÷ 4 = 150 units

Answer: 150 units

Example 2

The population of a town was 80,000 in 2015 and grew to 92,000 in 2020. Calculate the percentage increase over the 5‑year period.

Solution

1. Increase = 92,000 - 80,000 = 12,000
2. Percentage increase = (12,000 ÷ 80,000) × 100 = 0.15 × 100 = 15%

Answer: 15%

Example 3

A pie chart shows the market share of four brands: A – 25%, B – 35%, C – 20%, D – 20%. If the total market size is 8 lakh units, find the units sold by Brand B.

Solution

1. Convert percentage to decimal: 35% = 35 ÷ 100 = 0.35
2. Units for B = 0.35 × 8,00,000 = 2,80,000 units

Answer: 2,80,000 units

Example 4 (Mixed DI)

The table below gives the number of books sold by a publisher in three cities.

City — Jan — Feb — Mar

X — 120 — 150 — 130

Y — 80 — 90 — 100

Z — 200 — 180 — 210

Find the total books sold in February across all cities.

Solution

1. Add February values: 150 (X) + 90 (Y) + 180 (Z) = 420 books

Answer: 420 books

4. Shortcuts and tricks

• Row‑wise/column‑wise addition: When a table asks for a total of a row or column, add the numbers directly instead of writing a separate equation for each.
• Use the ‘difference’ method: For percentage change, compute the difference first, then divide by the original value – avoids mental fraction errors.
• Cross‑multiplication for ratios: If asked to find a missing part in a ratio, set up a proportion and use cross‑multiplication (a/b = c/d → a×d = b×c).
• Eliminate common factors: In large numbers, cancel zeros before performing multiplication or division to keep numbers small.
• Quick conversion: Remember 1% = 1/100, 5% = 1/20, 10% = 1/10 – use these to estimate percentages fast.

5. Common mistakes to avoid

• Skipping the unit conversion: Always check if the data is in different units (e.g., km vs. m) and convert before calculations.
• Reading the wrong row/column: In tables, double‑check the heading before picking a number.
• Sign errors in percentage change: Use (New - Old) not (Old - New) for increase; reverse for decrease.
• Rounding too early: Keep intermediate results exact; round only in the final answer to avoid cumulative errors.
• Misinterpreting ‘average’: Remember average = total ÷ count, not the middle value unless specifically asked for median.