Statistics and Probability
Tamil Nadu Board · Class 10 · Mathematics
Quick revision notes for Statistics and Probability — Tamil Nadu Board Class 10 Mathematics. Key concepts, formulas, and definitions for last-minute revision.
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Measures of Dispersion – Overview and Range
- Dispersion tells us how spread out the data values are from the central value (mean).
- Two datasets can have the same mean but very different spreads – dispersion helps identify this difference.
- Example: Batsman A and Batsman B both scored a mean of 40 runs in 10 matches, but A's scores were scattered (4 to 93) while B's scores were clustered (26 to 50).
Standard Deviation and Variance
- Standard Deviation (σ) is the positive square root of Variance (σ²).
- Variance is the mean of the squares of deviations from the arithmetic mean.
- Standard deviation gives a clearer picture of how far values are from the mean.
Coefficient of Variation
- Coefficient of Variation (C.V.) is a relative measure of dispersion – it has NO units.
- C.V. is used to compare the consistency of two or more datasets that may have different units or different scales.
- C.V. = (σ/x̄) × 100 percent
Probability – Fundamentals
- Probability measures the likelihood of occurrence of an event in a random experiment.
- A Random Experiment has: (i) all possible outcomes are known, (ii) exact outcome cannot be predicted in advance.
- Sample Space (S) is the set of ALL possible outcomes of a random experiment.
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