Learning these TS Inter 2nd Year Maths 2A Formulas Chapter 8 Measures of Dispersion will help students to solve mathematical problems quickly.
TS Inter 2nd Year Maths 2A Measures of Dispersion Formulas
→ Measures of Dispersion : Range, mean deviation, variance, standard deviation are some measures of dispersion.
→ Range is defined as the difference of maximum value and the minimum value of the data.
→ Mean Deviation for ungrouped distribution :
- Mean Deviation about the mean = \(\frac{1}{n}\)Σ|xi – x̄|
- Mean Deviation about median = \(\frac{1}{n}\)Σ|xi – Median|
→ Mean Deviation for grouped data :
- Mean Deviation about mean = \(\frac{1}{n}\)Σfi|xi – x̄|, where N = Σfi
- Mean Deviation about median = \(\frac{1}{n}\)Σfi|xi – Median|, where N = Σfi
→ Variance and Standard Deviation for ungrouped data
σ2 = \(\frac{1}{n}\)Σ(xi – x̄)2, σ = \(\sqrt{\frac{1}{n} \Sigma\left(x_i-\bar{x}\right)^2}\)
→ Variance and Standard Deviation of a discrete frequency distribution
σ2 = \(\frac{1}{N}\)Σfi(xi – x̄)2, σ = \(\sqrt{\frac{1}{N} \Sigma f_i\left(x_i-\bar{x}\right)^2}\)
→ Standard deviation of a continuous frequency distribution
σ = \(\frac{1}{N} \sqrt{N \Sigma f_i x_i^2-\left(\Sigma f_i x_i\right)^2}\)
or
σ = \(\frac{h}{N} \sqrt{N \Sigma f_i y_i^2-\left(\Sigma f_i y_i\right)^2}\), where yi = \(\frac{\left(x_i-A\right)}{h}\)
→ Coefficient of variation = \(\frac{σ}{x̄}\) × 100; x̄ ≠ 0.