Mathematics

Algebra, Statistics & Data Interpretation

Elementary algebra covers linear and quadratic equations, while DI tests how quickly you can read tables, bar graphs and pie charts. SSC and Banking exams give 5–10 marks for DI alone — usually 3-4 questions on a single chart, so accuracy multiplies.

Exam relevance: Banking exams (IBPS PO, SBI PO, RBI Grade B): 10–15 marks of DI + Caselets. SSC CGL Tier-II has 25-question DI+Stats sets. RRB exams test elementary algebra, mean/median/mode and bar-graph reading.

On this page

  1. Elementary Algebra (Linear & Quadratic Equations)
  2. Statistics — Mean, Median, Mode
  3. Data Interpretation (Bar Graphs, Pie Charts, Tables)

1Elementary Algebra (Linear & Quadratic Equations)

An equation is a statement that two expressions are equal. A linear equation has the highest power of x as 1; a quadratic equation has the highest power of x as 2.

Linear in one variable: ax + b = 0 → x = −b/a. Linear in two variables: solve by substitution or elimination. Quadratic: ax² + bx + c = 0 → x = [−b ± √(b² − 4ac)] / 2a (quadratic formula). Discriminant D = b² − 4ac: D > 0 → two real roots; D = 0 → equal roots; D < 0 → no real roots. Sum of roots = −b/a; product of roots = c/a.

Examples
  • Solve 3x − 7 = 2x + 5 → x = 12.
  • Solve x² − 5x + 6 = 0 → x = 2 or 3 (sum 5, product 6).
  • Solve 2x + 3y = 12, 3x − y = 7 → x = 3, y = 2.
  • If roots of x² + bx + 12 = 0 are 3 and 4 → sum = 7 → b = −7. ✓
Exam tip: If the question only asks for the sum or product of roots, use Vieta's formulas (−b/a and c/a) instead of solving.

2Statistics — Mean, Median, Mode

Mean is the arithmetic average; Median is the middle value when data is arranged in order; Mode is the value that occurs most frequently.

Mean = Sum of values / Number of values. Median: arrange the data in ascending order; if n is odd, median = middle value; if n is even, median = average of two middle values. Mode = the value with the highest frequency. For grouped data, use class-midpoints. Empirical relation: Mode = 3 × Median − 2 × Mean.

Examples
  • Data: 2, 4, 4, 6, 8 → Mean = 24/5 = 4.8; Median = 4; Mode = 4.
  • Data: 7, 5, 9, 11, 5, 8, 5 → Mode = 5 (appears thrice).
  • Data: 10, 20, 30, 40 (even count) → Median = (20+30)/2 = 25.
  • If Mean = 50 and Median = 48, then Mode = 3(48) − 2(50) = 44.
Exam tip: Mean is sensitive to extreme values; Median is not. For salaries or skewed data, Median is usually a better measure.

3Data Interpretation (Bar Graphs, Pie Charts, Tables)

Data Interpretation tests your ability to read information presented in bar graphs, line graphs, pie charts, tables or caselets and answer accuracy/speed questions on it.

Bar graph: compare heights/lengths to read absolute values. Pie chart: total = 360°; each slice's value = (slice angle/360) × total OR (slice %/100) × total. Table: read row and column headers carefully, then perform the asked computation. For 'percentage change' questions: ((New − Old)/Old) × 100. Always look for keywords: 'approximate', 'at least', 'at most', 'difference between' — they signal different operations.

Examples
  • Pie chart total = 7,200; slice for Rent = 90° → Rent = (90/360)×7200 = ₹1,800.
  • Bar graph shows sales of 2024 = 500 units, 2025 = 650 units → percentage growth = 150/500 ×100 = 30%.
  • Table: Boys = 240, Girls = 360 → ratio = 2:3, total students = 600.
  • Pie: 25% science, 30% commerce, 45% arts; 600 students total → arts = 270.
Exam tip: Before answering any question, glance at the chart's title, axis units, and legend. Misreading thousands as units is the single most common DI error.

Short Tricks & Shortcuts

Use these speed tricks in the exam. Each trick is followed by a worked example so you can verify the shortcut yourself.

Trick 1Vieta's — sum and product of quadratic roots

For ax² + bx + c = 0, sum of roots = −b/a, product of roots = c/a. Use these directly when the question only asks sum/product.

Example: Roots of x² − 7x + 12 = 0: sum = 7, product = 12 → roots are 3 and 4.
Trick 2Discriminant tells the root nature instantly

D = b² − 4ac. D > 0 → two distinct real roots; D = 0 → equal roots; D < 0 → no real roots (complex pair).

Example: For 2x² + 3x + 5 = 0, D = 9 − 40 = −31 < 0 → no real roots.
Trick 3Pie chart angle ↔ value

1% of total = 3.6° of central angle. Slice value = (angle/360) × Total = (%/100) × Total.

Example: Total budget ₹7,200, Rent slice 90° → Rent = (90/360) × 7200 = ₹1,800.
Trick 4Empirical formula relating Mean, Median, Mode

Mode = 3 × Median − 2 × Mean. Useful when one of the three is missing in moderately skewed data.

Example: If Mean = 50, Median = 48 → Mode ≈ 3(48) − 2(50) = 44.
Trick 5% change shortcut

% change = (New − Old) / Old × 100. Decrease gives a negative answer. Always divide by OLD value, never NEW.

Example: Sales up from 500 → 650 → growth = 150/500 × 100 = 30%.
Trick 6Median formula for grouped data (even count shortcut)

For an even number of observations, median = average of the two middle values after sorting. For odd count, it is simply the middle value.

Example: Data 10, 20, 30, 40 → median = (20+30)/2 = 25.

Quick Revision Facts

  • For a quadratic ax² + bx + c = 0: roots are real and distinct iff b² > 4ac.
  • In a pie chart: 1% = 3.6° of central angle.
  • For a frequency distribution, mode is the modal class midpoint or computed using the formula L + ((f₁−f₀)/(2f₁−f₀−f₂))×h.
  • For symmetric data, Mean = Median = Mode.

Frequently Asked Questions

Spend 30 seconds reading axes, units and legend before answering. Solve the easiest sub-question first to confirm you read the chart correctly, then attack percentage-change and ratio questions.

Yes — it has two complex roots given by the same formula with √(negative) treated as imaginary. Government exams rarely ask for complex roots in objective form.
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