Now,F2= 100 (Total Frquency) - (14+f1+27+15)OR F2 = 44-f1Calculation of Median
ExpenditureNo. of FamiliesCumulative Frequency0-20141420-40f114+f140-602741+f160-80f285+f1-f1=8580-10015100Median is given in this problem as 50Middle item of the series is also 100/2 is 50Which means it lies in the class-interval 40-60Now, Formula for Median is M=l1+l2−l1f1(m−c)50=40+60−4027[50−(14+f1)]50=40+2027[36+f1]F1 = 22.5Since the frequency in this position cannot be in fraction so f1 would be taken as 23.F2=44-f1 or 44-23 or 21Thus the missing values in the question are 23 and 21.Practice Example 32An incomplete distribution is given belowVariable Frequency10-201220-303030-40?40-506550-60?
60-702570-8018Total Frequency229(Answer: missing frequencies are 34 and 45, mean = 45.83)Calculation of Median in Open End Series Example 33You are given below a certain statistical distributionValueFrequencyLess than 10040100-20089200-300148300-40064400 and above39Calculate the most suitable average giving reasons for your choice. (Answer: Median = 241.2)[Hint: since the series has open ends, we cannot calculate mean. Median would be the most suitableaverage in such a case.]Merits of Median1.It is easily understood2.It is not affected by extreme values3.It can be located graphically4.It is the best measure for qualitative data such as beauty, intelligence, honesty etc.5.It can be easily located even if the class-intervals in the series are unequal6.It can be determined even by inspection in many casesDrawbacks of Median 1.It is not subject to algebraic treatments2.It cannot represent the irregular distribution series3.It is positional average and is based on the idle item4.It does not have sampling stability5.It is an estimate in case of a series containing even number of items6.It does not take into account the values of all the items in the series7.It is not suitable in those cases where due importance and weight should be given to extremevalues
Uses of Median1.It is useful in those cases where numerical measurements are not possible2.It is also useful in those cases where mathematical calculations cannot be made in order toobtain the mean3.It is generally used in studying phenomena like skill, honesty, intelligence, etc. Computation of Quartile, Deciles and Percentiles in Series of Individual ObservationsIn a series of individual observations and in a discrete series, the values of the lower (Q1) and the upper (Q3) quartiles would be the value of (N+14)th∧3(N+1)4thitems respectively. The values of decile in such series would be as followsD1=value of(N+110)thitemD2=value of2(N+110)thitemAnd so on.The values of percentile would be P1=valueof(N+1100)thitemP40=valueof40(N+1100)thitemIn continuous series, in the calculation of quartiles, deciles and percentiles N+14,N+110,N+1100would be replaced by N4,N10,N100respectively. The values would have to be interpolated here as was done in case of the computation of median. The following examples would illustrate the above points.