Now F2 100 Total Frquency 14f12715 OR F2 44 f1 Calculation of Median

Now f2 100 total frquency 14f12715 or f2 44 f1

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Now, F2= 100 (Total Frquency) - (14+f1+27+15) OR F2 = 44-f1 Calculation of Median
Expenditure No. of Families Cumulative Frequency 0-20 14 14 20-40 f1 14+f1 40-60 27 41+f1 60-80 f2 85+f1-f1=85 80-100 15 100 Median is given in this problem as 50 Middle item of the series is also 100/2 is 50 Which means it lies in the class-interval 40-60 Now, Formula for Median is M = l 1 + l 2 l 1 f 1 ( m c ) 50 = 40 + 60 40 27 [ 50 ( 14 + f 1 ) ] 50 = 40 + 20 27 [ 36 + f 1 ] F1 = 22.5 Since the frequency in this position cannot be in fraction so f1 would be taken as 23. F2=44-f1 or 44-23 or 21 Thus the missing values in the question are 23 and 21. Practice Example 32 An incomplete distribution is given below Variable Frequency 10-20 12 20-30 30 30-40 ? 40-50 65 50-60 ?
60-70 25 70-80 18 Total Frequency 229 (Answer: missing frequencies are 34 and 45, mean = 45.83) Calculation of Median in Open End Series Example 33 You are given below a certain statistical distribution Value Frequency Less than 100 40 100-200 89 200-300 148 300-400 64 400 and above 39 Calculate 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 suitable average in such a case.] Merits of Median 1. It is easily understood 2. It is not affected by extreme values 3. It can be located graphically 4. 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 unequal 6. It can be determined even by inspection in many cases Drawbacks of Median 1. It is not subject to algebraic treatments 2. It cannot represent the irregular distribution series 3. It is positional average and is based on the idle item 4. It does not have sampling stability 5. It is an estimate in case of a series containing even number of items 6. It does not take into account the values of all the items in the series 7. It is not suitable in those cases where due importance and weight should be given to extreme values
Uses of Median 1. It is useful in those cases where numerical measurements are not possible 2. It is also useful in those cases where mathematical calculations cannot be made in order to obtain the mean 3. It is generally used in studying phenomena like skill, honesty, intelligence, etc. Computation of Quartile, Deciles and Percentiles in Series of Individual Observations In 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 + 1 4 ) th 3 ( N + 1 ) 4 th items respectively. The values of decile in such series would be as follows D 1 = value of ( N + 1 10 ) thitem D 2 = value of 2 ( N + 1 10 ) thitem And so on. The values of percentile would be P 1 = valueof ( N + 1 100 ) thitem P 40 = valueof 40 ( N + 1 100 ) thitem In continuous series, in the calculation of quartiles, deciles and percentiles N + 1 4 , N + 1 10 , N + 1 100 would be replaced by N 4 , N 10 , N 100 respectively. 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.

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