📐 CENTRAL TENDENCY FORMULA SHEET
Mean, Median & Mode — Memory Hacks & Shortcuts for DCET 5 GUARANTEED MARKS
The Empirical Relationship (The 5-Second DCET Hack!)
Mode = 3 × Median − 2 × Mean
🧠 How to NEVER forget this:
• Median has 6 letters (M-e-d-i-a-n) → gets the bigger number (3)
• Mean has 4 letters (M-e-a-n) → gets the smaller number (2)
Dodda word-ge dodda number, sanna word-ge sanna number! ✅
📝 DCET-Style Problem #1 — Empirical Relationship
Q: In a moderately skewed distribution, if Mean = 10 and Median = 12, find the Mode.
(A) 14
✅ (B) 16
(C) 18
(D) 20
Mode = 3 × Median − 2 × Mean
Mode = 3 × 12 − 2 × 10 = 36 − 20 = 16 ✅
⏱️ Time taken: 10 seconds!
📝 DCET-Style Problem #2 — Standard Deviation Shortcut
Q: What is the Standard Deviation of 7, 7, 7, 7, 7?
(A) 7
(B) 1
✅ (C) 0
(D) 49
⚡ Instant Rule: If ALL values are the same → SD = 0 (ALWAYS!).
No deviation = No formula needed. Variance = 0, SD = 0. ✅
📋 Quick Reference: Central Tendency at a Glance
| Property | Mean | Median | Mode |
|---|
| Affected by outliers? | ✅ Yes (sensitive) | ❌ No (robust) | ❌ No |
| Works with grouped data? | ✅ Yes | ✅ Yes | ✅ Yes |
| Can there be multiple values? | ❌ No (unique) | ❌ No (unique) | ✅ Yes (bimodal/multimodal) |
| Sum of deviations from it = 0? | ✅ Yes (only Mean) | ❌ No | ❌ No |
| DCET Weightage | 2+ Marks | 1-2 Marks | 1-2 Marks |
📐 Bonus: Measures of Dispersion Quick Formulas
Range
Range = Max Value − Min Value
Simplest measure. Just subtract!
Variance (σ²)
σ² = Σ(x − x̄)² / n
Average of squared deviations from mean.
Standard Deviation (σ)
σ = √Variance = √(σ²)
Square root of Variance. Same unit as data.
Quartile Deviation
QD = (Q3 − Q1) / 2
Half the inter-quartile range.