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Grouping can be in the form of a discrete frequency

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Unformatted text preview: sum of the frequency of the class and the frequencies of the pervious classes, ie adding the frequencies successively, so that the last cumulative frequency gives the total number of items. 108 Discrete Series: Step1: Find cumulative frequencies. N +1 Step2: Find 2 Step3: See in the cumulative frequencies the value just greater than N +1 2 Step4: Then the corresponding value of x is median. Example 14: The following data pertaining to the number of members in a family. Find median size of the family. Number of members x Frequency F 1 2 3 4 5 6 7 8 9 10 11 12 1 3 5 6 10 13 9 5 3 2 2 1 Solution: X 1 2 3 4 5 6 7 8 9 10 11 12 f 1 3 5 6 10 13 9 5 3 2 2 1 60 Median = size 109 cf 1 4 9 15 25 38 47 52 55 57 59 60 N +1 of 2 th item 60 + 1 th = size of item 2 = 30.5th item The cumulative frequencies just greater than 30.5 is 38.and the value of x corresponding to 38 is 6.Hence the median size is 6 members per family. Note: It is an appropriate method because a fractional value given by mean does not indicate the average number of members in a family. Continuous Series: The steps given below are followed for the calculation of median in continuous series. Step1: Find cumulative frequencies. N Step2: Find 2 Step3: See in the cumulative frequency the value first greater than N 2 , Then the corresponding class interval is called the Median class. Then apply the formula N −m Median = l + 2 ×c f Where l = Lower limit of the median class m = cumulative frequency preceding the median c = width of the median class f =frequency in the median class. N=Total frequency. Note : If the class intervals are given in inclusive type convert them into exclusive type and call it as true class interval and consider lower limit in this. Example 15: 110 The following table gives the frequency distribution of 325 workers of a factory, according to their average monthly income in a certain year. Income group (in Rs) Number of workers 1 Below 100 20 100-150 42 150-200 55 200-250 62 250-300 45 300-350 30 350-400 25 400-450 15 450-500 18 500-550 10 550-600 2 600 and above 325 Ca...
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