Calculation of median individual series step 1

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Calculation of median Individual series : Step-1: Arrange the data in ascending or descending order of magnitude.
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50 Step-2: Case-i If the number of observations is odd then median is the th n 2 1 observation in the arranged order. Case-ii If the number of observations is even then the median is the mean of th n 2 and th n 1 2 observations in the arranged order. Example: Find the median of the following data: 12, 2, 16, 8, 14, 10, 6 Step 1: Organize the data, or arrange the numbers from smallest to largest. 2, 6, 8, 10, 12, 14, 16 Step 2: Since the number of data values is odd, the median will be found in the position. Step 3: In this case, the median is the value that is found in the fourth position of the organized data. 2, 6, 8, 10 , 12, 14, 16 Example: Find the median of the following data: 7, 9, 3, 4, 11, 1, 8, 6, 1, 4 Step 1: Organize the data, or arrange the numbers from smallest to largest. 1, 1, 3, 4, 4, 6, 7, 8, 9, 11 Step 2: Since the number of data values is even, the median will be the mean value of the numbers found before and after the position. Step 3: The number found before the 5.5 position is 4 and the number found after the 5.5 position is 6. Now, you need to find the mean value. 1, 1, 3, 4, 4, 6, 7, 8, 9, 11 Calculation of median-Discrete series: Step-i: Arrange the data in ascending or descending order of magnitude. Step-ii: find out the cumulative frequency (c.f) Step-iii: Apply the formula: Median = size of 2 1 N
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51 Step-iv: Now look at the cumulative frequency column and find that total which is either equal to 2 1 N or next higher to that and determine the value of the variable corresponding to it. That gives the value of median. Computation of median-Continuous series: The median of a continuous series can be calculated by the below interpolation formula. Median =   c f m N l 2 / Where l = lower limit of the median class. C = Size of the class f = frequency corresponding to the median class N = total frequency M = cumulative frequency of the class preceding to the median class. Mode: The mode or the modal value is that value in a series of observations which occurs with the greatest frequency. Ex: The mode of the series 3, 5,8,5,4,5,9,3 would be 5. In certain cases there may not be a mode or there may be more than one mode. Ex : 1) 40, 44,57,78,84 (no mode) 2) 3, 4, 5, 5, 4, 2, 1 (modes 4 and 5) 3) 8, 8, 8, 8, 8 (no mode) A series of data which having one mode is called ‘unimodal’ and a series of data which having two modes is called ‘bimodal’ . It may also have several modes and be called ‘multimodal’ . Calculation of mode continuous series: In a continuous series, to find out the mode we need one step more than those used for discrete series. As explained in the discrete series, modal class is determined by inspection or by preparing grouping and analysis tables. Then we apply the following formula.
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