58 21834 harmonic mean for continuous series 1

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Unformatted text preview: = 100/ 4.58 = 21.834 Harmonic mean for continuous series 1. Calculate harmonic mean for the given data. Class : 10-20 Frequency : 20-30 30-40 40-50 50-60 60-70 7 3 15 12 8 5 Class Frequency Mid x 1/x F . 1/x 10-20 5 15 .0661 .33 20-30 7 25 .04 .28 30-40 3 35 .0285 .085 40-50 15 45 .0222 .333 50-60 12 55 .0181 .218 50-60 8 65 .0153 .123 f ( 1/x) =1.369 f =50 HM = N / (1/x) HM = 50 / 1.369 = 37.8689 Median Median is the middlemost item of a given series. In individual series, we arrange the given data according to ascending or descending order and take the middlemost item as the median. When two values occur in the middle, we take the average of these two values as median. Since median is the central value of an ordered distribution, there occur equal number of values to the left and right of the median. Individual series Median = (N+ 1 / 2) th item Sikkim Manipal University Page No. 177 Research Methodology Unit 11 Illustration 1. Find the median of the following scores. 97 50 95 51 65 80 70 90 60 85 64 81 75 First we arrange the series according to ascending order. 50 51 60 64 85 90 95 97 Median 65 70 75 80 81 69 80 80 85 = (N+ 1) / 2 th item = (13+ 1) / 2 th item = (14 / 2) th item = (7) th item = 75 Median for distribution with even number of items 2. Find the median of the following data. 95 51 91 70 78 60 90 64 85 75 First we arrange the series according to ascending order. 51 60 64 90 91 95 Median 69 70 75 78 = (N+ 1) / 2 th item = (12+ 1) / 2 th item = (13 / 2) th item = (6.5) th item = (6th item + 7th item) / 2 = (75 + 78) / 2 = 153/2 = 76.5 Sikkim Manipal University Page No. 178 Research Methodology Unit 11 Median for Discrete Series To find the median of a grouped series, we first of all, cumulate the frequencies. Locate median at the size of (N+ 1) / 2 th cumulative frequency. N is the cumulative frequency taken. Steps 1. Arrange the values of the data in ascending order of magnitude. 2. Find out cumulative frequencies 3. Apply the formula (N+ 1) / 2 th item 4. Look at the...
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