A Note The step deviation method is applied to compute x . Rest of the procedure is same. (ii) Mean deviation about median The process of finding the mean deviation about median for a continuous frequency distribution is similar as we did for mean deviation about the mean. The only difference lies in the replacement of the mean by median while taking deviations.
Let us recall the process of finding median for a continuous frequency distribution. The data is first arranged in ascending order. Then, the median of continuous frequency distribution is obtained by first identifying the class in which median lies (median class) and then applying the formula STATISTICS frequency N C Median l f = + × where median class is the class interval whose cumulative frequency is just greater than or equal to N , N is the sum of frequencies, l , f , h and C are, respectively the lower limit , the frequency, the width of the median class and C the cumulative frequency of the class just preceding the median class. After finding the median, the absolute values of the deviations of mid-point x i of each class from the median i.e., M i x − are obtained.
Then M.D. (M) M N f x ∑ The process is illustrated in the following example: Example Calculate the mean deviation about median for the following data : Class - - - - - - Frequency Solution Form the following Table . from the given data : Table . Class Frequency Cumulative Mid-points Med.
xi − f i Med. xi − f i ( c.f. ) x i - - - - - - MATHEMATICS The class interval containing th N or th item is - . Therefore, – is the median class.
We know that Median = N C l f × Here l = , C = , f = , h = and N = Therefore, Median × = + = Thus, Mean deviation about median is given by M.D. (M) = M N f x