( N = f i )

( N = f i ) (ii) Shortcut method (or) Step deviation method To make the calculation simple, we provide the following formula. Let A be the assumed mean, x i be the middle value of the i th class and c is the width of the class interval. d i = s = fd N fd N Σ Σ Example . Marks of the students in a particular subject of a class are given below.

Find its standard deviation. Marks - - - - - - - Number of students Solution Let the assumed mean, A = , c = Marks Mid value x i f i d i = x i –A fd fd - - - - - - - - - - – – – – – – N = Σ fd i = − Σ fd Standard deviation s = × fd N fd N Σ Σ s = −−  ; s  . Thinking Corner . The standard deviation of a data is .

, if is added to all the data values then the new standard deviation is . . If S is the standard deviation of values p , q , r then standard deviation of p – , q – , r – is . Example .

The mean and standard deviation of observations are found to be and respectively. On rechecking it was found that one of the observation with value was incorrect. Calculate the correct mean and standard deviation if the correct observation value was ? Solution n = , x = , s = ; x = Σ x n ; S x = Wrong observation value = , Correct observation value = .

Correct total = Statistics and Probability Correct mean x Standard deviation s  Σ Σ Incorrect value of s