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|x
_{i}– x̄| - Mean Deviation about median = \(\frac{1}{n}\)Σ|x
_{i}– Median|

→ Mean Deviation for grouped data :

- Mean Deviation about mean = \(\frac{1}{n}\)Σf
_{i}|x_{i}– x̄|, where N = Σf_{i} - Mean Deviation about median = \(\frac{1}{n}\)Σf
_{i}|x_{i}– Median|, where N = Σf_{i}

→ Variance and Standard Deviation for ungrouped data

σ^{2} = \(\frac{1}{n}\)Σ(x_{i} – x̄)^{2}, σ = \(\sqrt{\frac{1}{n} \Sigma\left(x_i-\bar{x}\right)^2}\)

→ Variance and Standard Deviation of a discrete frequency distribution

σ^{2} = \(\frac{1}{N}\)Σf_{i}(x_{i} – 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 y_{i} = \(\frac{\left(x_i-A\right)}{h}\)

→ Coefficient of variation = \(\frac{σ}{x̄}\) × 100; x̄ ≠ 0.