 # Assumptions regarding the size of the class interval

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assumptions regarding the size of the class interval of the open-endedclasses. In an extremely asymmetrical distribution, it is not a good measure ofcentral tendency.171 | PageRESEARCH METHODOLOGY
172 | Page2. MedianThe median can be computed for ratio, interval or ordinal scale data. Themedian is that value in the distribution such that 50per cent of theobservations are below it and 50 per cent are above it. The median for theungrouped data is deﬁned as the middle value when the data is arranged inascending or descending order of magnitude. In case the number of items inththe sample is odd, the value of (n+ 1)/2 item gives the median. However ifthere are even number of items in the sample,say of size 2n,the arithmeticththmean ofnand (n+ 1)items gives the median. It is again emphasized that dataneeds to be arranged in ascending or descending orders of magnitude beforecomputing the median.Given below are a few examples to illustrate the computation of median:Example 9.2:The marks of 21 students in economics are given 62, 38, 42,43, 57, 72, 68, 60, 72, 70, 65, 47, 49, 39, 66, 73, 81, 55, 57, 57 and 59. Computethe median of the distribution.Solution:By arranging the data in ascending order of magnitude, we obtain: 38, 39,42, 43, 47, 49, 55, 57, 57, 57, 59, 60, 62, 65, 66, 68, 70, 72, 72, 73 and 81.thThe median will be the value of the 11 observation arranged as above.Therefore,the value of median equals 59.This means 50per cent of studentsscore marks below 59 and 50 per cent score above 59.The median could also be computed for the grouped data. In that case, ﬁrst ofall, median class is located and then median is computed using interpolationby using the assumption that all items are evenly spread over the entire classinterval. The median for the grouped data is computed using the followingformula:Where,l=Lower limit of the median classf=Frequency of the median classCF=Cumulating frequency for the class immediately below the classcontaining the medianh= size of the interval of the median class.Given below is an example to illustrate the computationof median in the case of grouped data:Example 9.3:The distribution of dividend declared by seventy-sevencompanies is given in the following table.Compute the median of thedistribution.RESEARCH METHODOLOGY
Solution:Where,l=Lower limit of the median class = 30f=Frequency of the median class = 18CF=Cumulating frequency for the class immediately below the classcontaining the median = 37h= Size of the interval of the median class =10Substituting these values in the formula for median, we getMedian = 30.83The results show that half of the companies have declared less than30.83 per cent dividend and the other half have declared more than 30.83 percent dividend.The limitation of median as a measure of central tendency is that it does notuse each and every observation in its computation since it is a positionalaverage.

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