13Class 11 Maths

Statistics formulas

Mean deviation, variance and standard deviation formulas for Statistics. Questions here are mostly careful calculation, so set out a table.

Free from Anva, anvatechlabs.com

Mean deviation

Ungrouped data: $\displaystyle \text{M.D.}(a) = \frac{\sum|x_i - a|}{n}$
a is the mean or median.
Grouped data: $\displaystyle \text{M.D.}(a) = \frac{\sum f_i|x_i - a|}{N}, \quad N = \sum f_i$

Variance: $\displaystyle \sigma^2 = \frac{\sum(x_i - \bar x)^2}{n}$
Shortcut form: $\displaystyle \sigma^2 = \frac{\sum x_i^2}{n} - \left(\frac{\sum x_i}{n}\right)^2$
Grouped data: $\displaystyle \sigma^2 = \frac{\sum f_i(x_i - \bar x)^2}{N}$
Step-deviation method: $\displaystyle \sigma^2 = h^2\left[\frac{\sum f_iy_i^2}{N} - \left(\frac{\sum f_iy_i}{N}\right)^2\right], \quad y_i = \frac{x_i - A}{h}$
Coefficient of variation: $\displaystyle \text{C.V.} = \frac{\sigma}{\bar x}\times100$
Lower means more consistent.

Forgetting the h² when converting step-deviation back to variance.
Comparing consistency using σ alone when the means differ. Use the coefficient of variation.

7 days free when you sign up. No card needed.