Look at the cumulative frequency column and find the

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Unformatted text preview: cumulative frequency column and find the value of the variable corresponding to the above. Find median for the following data. Income : 100 150 80 200 250 180 Number of persons : 24 26 16 20 6 30 First of all arrange the data according to ascending order. Income Frequency Cum. Frequency 80 16 100 24 40 150 26 (N+ 1) / 2 66 180 30 96 200 20 116 250 Median 16 6 122 = (N+ 1) / 2 th item = (122+ 1) / 2 th item = (123) / 2 th item = (61.5) th item = Value at the 61.5 cumulative frequency is taken as median Therefore Median = 150 Sikkim Manipal University Page No. 179 Research Methodology Unit 11 Median for Continuous Series To find the median of a grouped series, with class interval, we first of all, cumulate the frequencies. Locate median at the size of (N) / 2 th cumulative frequency. Apply the interpolation formula to obtain the median Median = L1 + (N/2 – m) / f X C L1 = Lower limit of the median Class N/2 = Cumulative frequency/ 2 m = Cumulative frequency of the class preceding the median class f = frequency of the median class C = Class interval Find median of the following data. Class : 12-14 15-17 18-20 21-23 24-26 Frequency : 1 3 8 2 6 Class Frequency CF 12-14 1 1 15-17 3 4 18-20 8 12 (N/2 = 10) 21-23 2 14 24-26 6 20 Median = L1 + (N/2 – m) / f X C L1 = 18 N/2 = 10 m = 4 f = 8 C = 2 = 18+ (10 – 4) / 8 X 2 = 18 + 6/8 X 2 = 18 + (12/8) = 18 + 1.5 = 19.5 Sikkim Manipal University Page No. 180 Research Methodology Unit 11 Merits of Median 1. Median is easy to calculate and simple to understand. 2. When the data is very large median is the most convenient measure of central tendency. 3. Median is useful finding average for data with open-ended classes. 4. The median distributes the values of the data equally to either side of the median. 5. Median is not influenced by the extreme values present in the data. 6. Value of the median can be graphically determined. Demerits of Median To calculate median, data should be arranged according to ascending order. This is tedious when t...
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