Statistic Formula | Class 11 and 12 Mathematics

Statistics Formula

Arithmetics Mean

The arithmetic mean (or simple mean) of a set of observations is obtained by dividing the sum of the values of observations by the number of observations.

(i) Arithmetic Mean for unclassified (Ungrouped or Raw) Data

\bar{x} = {x_1+x_2+...+x_n\over n}={ \sum_{i=1}^{n}{x_i} \over n}

(ii) Arithmetic Mean for Discrete Frequency Distribution

Variate (x) x1 x2 xn
Frequency (f) f1 f2 fn

.\bar{x} = {x_1f_1+x_2f_2+...+x_nf_n\over f_1+f_2+...+f_n}

or, \bar{x} ={ \sum_{i=1}^{n}{x_if_i} \over \sum_{i=1}^{n}{f_i} }

(iii) Arithmetic Mean for Grouped Frequency Distribution

Class mark (y) y1 y2 yn
Frequency (f) f1 f2 fn

(a) From Direct Method: \bar{x} ={ \sum_{i=1}^{n}{x_if_i} \over \sum_{i=1}^{n}{f_i} }

(b) Shortcut or Deviation: \bar{x} = A + { \sum_{i=1}^{n}{d_if_i} \over \sum_{i=1}^{n}{f_i} }×h


  • A = Assumed mean
  • d = deviation
  • h = class width
  • x = class mark or mid-value

(c) Step-deviation: \bar{x} = A + { \sum_{i=1}^{n}{u_if_i} \over \sum_{i=1}^{n}{f_i} }×h


  • A = Assumed mean
  • u = x - A\over h

(d) Combined Mean: If \bar{x}_1 and \bar{x}_2 are means of n1 and n2 observation respectively then,

Combined mean \bar{X} = n_1 × \bar{x}_1 + n_2 × \bar{x}_2\over n_1 + n_2

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