Statistics
Board: CBSE |Class:Class11
ComprehensivestudynotesforStatisticsbyAjayYadav(MathKingofKatargam).
Range=Max-Min.Meandeviation,variance,andstandarddeviationmeasurespreadofdata.
MDaboutmean=Σ|x₅-x̄|/n(ungrouped).Forgrouped:Σf|x₅-x̄|/Σf.Alsoaboutmedian:Σ|x₅-M|/n.
Variance(σ²)=Σ(x₅-x̄)²/n(ungrouped).Forgrouped:Σf(x₅-x̄)²/Σf.SD(σ)=√Variance.
Variance=Σxˡˡ/n-(x̄)².Also:σ²=(Σfxˡˡ/Σf)-(Σfxˡ/Σf)².
CV=(σ/x̄)×100%.Usedtocomparevariabilityoftwodatasets.LowerCVmeansmoreconsistent/stabledata.
| MDaboutmean | MD=Σ|x₅-x̄|/n |
| Variance (ungrouped) | σ² = Σ(x₅-x̄)²/n |
| SD | σ = √σ² |
| CV | CV = (σ/x̄)×100% |
Solved Examples
Example 1: Find variance of 2, 4, 6, 8, 10.
Solution: x̄=6. Σ(x-x̄)² = 16+4+0+4+16=40. σ²=40/5=8. σ=2√2.
Example 2: Find coefficient of variation: x̄=50, σ=5.
Solution: CV = (5/50)×100 = 10%.
Practice Questions
- Find mean deviation about mean for: 3, 6, 9, 12, 15.
- Find variance and SD: 10, 20, 30, 40, 50.
- Compare: Team A (x̄=70, σ=5) vs Team B (x̄=60, σ=4). Which is more consistent?
- Find variance of grouped data: CI 0-10(3), 10-20(7), 20-30(10), 30-40(5).
- If CV=15% and x̄=80, find σ.
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