NEB Class 12 • Mathematics • Statistics • Concept Guide

Karl Pearson & Spearman Correlation: NEB Class 12 Maths Guide

Master Karl Pearson and Spearman Correlation through clear concepts, representations, a reliable answer method and exam-focused practice.

ConceptsWorked reasoningNEB practice

Core concept

What Karl Pearson and Spearman Correlation means physically

Correlation quantifies association, not causation. Pearson measures linear association between numerical variables, while Spearman measures monotonic association through ranks and is less tied to linear scale.

Pearson r=Σ[(x−x̄)(y−ȳ)]/√[Σ(x−x̄)²Σ(y−ȳ)²]. Without ties, Spearman ρ=1−6Σd²/[n(n²−1)].

The institutional reference gives the wider physical model; the CDC curriculum determines the NEB boundary.

Worked checkpoint with interpretation

If two rankings of four students differ by squared-rank differences totaling 2, ρ=1−12/60=0.8.

Do not stop at the number. State what the sign, ratio, spacing, frequency or direction means. A common error is Claiming correlation proves cause, using Pearson for a strongly nonlinear pattern, mishandling tied ranks, or interpreting r=0 as no relationship of any kind.

NEB answer method

Model → evidence → equation → check

First identify the system and what the question asks. Label the diagram, apparatus or reaction with SI quantities, then state the principle before selecting an equation. Solve symbolically where possible and check units, limiting cases and chemical or physical meaning.

Stage	Question	Evidence
Model	What is idealised?	Assumption stated
Representation	Which diagram fits?	Labels or balanced equation
Calculation	Which relation follows?	Symbols then SI values
Evaluation	Does it make sense?	Unit, sign and trend check

Make the idea concrete in Nepal

Connect the model to a school laboratory, household technology, health, environment, energy or local material. The example should clarify the science rather than merely mention a place. Compare a prediction with an observation and record uncertainty.

Review the NEB Class 12 Mathematics revision roadmap and the complete Mathematics guide. For online or physical tuition, call 9846662070.

Frequently asked questions

Questions students ask about Karl Pearson and Spearman Correlation

What is the central idea of Karl Pearson and Spearman Correlation?+

Which equation should I remember?+

Pearson r=Σ[(x−x̄)(y−ȳ)]/√[Σ(x−x̄)²Σ(y−ȳ)²]. Without ties, Spearman ρ=1−6Σd²/[n(n²−1)].

How should I begin a numerical?+

Draw the situation, list known quantities in SI units, choose the governing relation symbolically, substitute once and finish with a unit and reasonableness check.

What is a common exam mistake?+

Claiming correlation proves cause, using Pearson for a strongly nonlinear pattern, mishandling tied ranks, or interpreting r=0 as no relationship of any kind.

How can I practise this topic?+

Alternate one concept explanation, one diagram and two numericals. Revisit errors after a day instead of only rereading the solution.

Where can I get tuition support?+

For online or physical KTM Tuition classes, call 9846662070. After Grade 12, the MKS Education panel below gives preparation and pre-counselling contacts.

References and next steps

Scope checked against CDC Nepal; concept support from an institutional reference and OpenStax Science. Continue with the Karl Pearson and Spearman Correlation cluster.

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