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If the number of values are odd median is the middle

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Unformatted text preview: er of values are given. Find median for the following data 25, 18, 27, 10, 8, 30, 42, 20, 53 Solution: Arranging the data in the increasing order 8, 10, 18, 20, 25, 27, 30, 42, 53 The middle value is the 5th item i.e., 25 is the median Using formula n + 1 th Md = item. 2 9 +1 = 2 th item. 10 = th item 2 = 5 th item = 25 Example 12 : 106 When even number of values are given. Find median for the following data 5, 8, 12, 30, 18, 10, 2, 22 Solution: Arranging the data in the increasing order 2, 5, 8, 10, 12, 18, 22, 30 Here median is the mean of the middle two items (ie) mean of (10,12) ie 10 + 12 = = 11 2 ∴median = 11. Using the formula n + 1 th Median = item. 2 2 8 + 1 th = item. 2 9 = th item = 4.5 th item 2 1 = 4th item + (5th item – 4th item) 2 1 = 10 + [12-10] 2 1 = 10 + × 2 2 = 10 +1 = 11 Example 13: The following table represents the marks obtained by a batch of 10 students in certain class tests in statistics and Accountancy. Serial No 1 2 3 4 107 5 6 7 8 9 10 Marks (Statistics) Marks (Accountancy) 53 55 52 32 30 60 47 46 35 28 57 45 24 31 25 84 43 80 32 72 Indicate in which subject is the level of knowledge higher ? Solution: For such question, median is the most suitable measure of central tendency. The mark in the two subjects are first arranged in increasing order as follows: Serial No Marks in Statistics Marks in Accountancy 1 28 2 30 3 32 4 35 5 46 6 47 7 52 8 53 9 55 10 60 24 25 31 32 43 45 57 72 80 84 n + 1 th 10 + 1 th th Median = item = item =5.5 item 2 2 Value of 5th item + value of 6th item = 2 46 + 47 Md (Statistics) = = 46.5 2 43 + 45 = 44 Md (Accountancy) = 2 There fore the level of knowledge in Statistics is higher than that in Accountancy. Grouped Data: In a grouped distribution, values are associated with frequencies. Grouping can be in the form of a discrete frequency distribution or a continuous frequency distribution. Whatever may be the type of distribution , cumulative frequencies have to be calculated to know the total number of items. Cumulative frequency : (cf) Cumulative frequency of each class is the...
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