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### Middle/High School Algebra, Geometry, and Statistics (AGS)9.22 Median of Discrete Values

 Median When the observation in the data are arranged in the order (ascending or descending), the median is the middle-value. That is 50% of the observations are below the median and 50% are above it. Following are the steps to find the median of an ungrouped frequency distribution Step 1. Arrange the variates in the ascending order of their magnitude. Step 2. Find the total number of variates, say n. Step 3. If n is odd then the median is the value of [(n+1)/2]th item. If n is even then the median is the A.M. of the values of (n/2)th and [(n/2) +1]th items. Example Find the median of the following observations i)15,40,25,16,28,32,36,42,16,19,28 ii)72,68,42,33,35,39,40,41,65,69 Solution i)Arranging the given data in the ascending order we get 15,16,16,19,25,28,28,32,36,40,42 Here n = 11(odd) Median = Value of the [(11+1)/2] th item = Value of the 6th item. So Median = 28 ii)Arranging the given data in the ascending order we get 33,35,39,40,41,42,65,68,69,72. Here n = 10(even) Median = Value of the A.M. of (n/2)th and [(n/2)+1]th item = A.M. of the values of the 5th and the 6th items. So Median = (41+42)/2 = 41.5 Merits of the median 1.) It can be calculated graphically. 2.) It is not affected by extreme values. 3.) It can be determined by inspection in many cases. Demerits of the median 1.) It is not directly based on all the values. 2.) It is not as stable as the arithmetic mean.
 Q 1: Numbers 50,42,41,35,2x+10,2x-8,12,11,8,6 are written in descending order and if their median is 25, find x.18151312 Q 2: The following data have been arranged in the ascending order : 24, 27, 28, 31, 34, x, 37, 40, 42, 45 In the above data, if 45 is changed to 33, find the new median.3632.53033.5 Q 3: The following data have been arranged in an ascending order : 12, 14, 17, 20, 22, x, 26, 28, 32, 36. If the median of the data is 23, find x.32222624 Q 4: Find the median for the following data. 46, 64, 87, 41, 58, 77, 35, 90, 55, 33, 92. If in the data, the observation 92 is replaced by 19, determine the new median. 55, new median = 5358, new median = 5558, new median = 5057, new median = 50 Q 5: The following observations have been arranged in the ascending order. If the median of the data is 63, find the value of x. 29, 32, 48, 50, x, x+2, 72, 78, 84, 95.62785663 Q 6: {1, 2, 3, 6, 8} is a set of 5 positive integers whose mean is 4 and median is 3. Write down another set of 5 positive integers, each having the same mean and median as this set. {1, 2, 3, 6, 10}{1, 2, 3, 4, 10} or {1, 2, 3, 5, 9}{1, 2, 3, 4, 11}{1, 2, 4, 5, 9} Question 7: This question is available to subscribers only! Question 8: This question is available to subscribers only!

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