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# F 4 7 9 13 18 20 24 25 625th item 4 th n 1 24

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Unformatted text preview: erval 4 rd is called 3 quartile class. Then apply the respective formulae N − m1 Q1 = l1 + 4 × c1 f1 N 3 − m3 4 Q3 = l3 + × c3 f3 Where l1 = lower limit of the first quartile class f1 = frequency of the first quartile class c1 = width of the first quartile class m1 = c.f. preceding the first quartile class l3 = 1ower limit of the 3rd quartile class f3 = frequency of the 3rd quartile class c3 = width of the 3rd quartile class m3 = c.f. preceding the 3rd quartile class Example 24: The following series relates to the marks secured by students in an examination. Marks No. of students 0-10 11 10-20 18 20-30 25 30-40 28 40-50 30 50-60 33 60-70 22 70-80 15 80-90 12 90-100 10 123 Find the quartiles Solution : C.I. 0-10 10-20 20-30 30-40 40-50 50-60 60-70 70-80 80-90 90-100 Q1 Q3 f 11 18 25 28 30 33 22 15 12 10 204 cf 11 29 54 82 112 145 167 182 194 204 N N 204 3 = = 51 4 4 4 N − m1 4 = l1 + × c1 f1 51 − 29 = 20 + × 10 = 20 + 8.8 = 28.8 25 N 3 − m3 4 = l3 + × c3 f3 = 60 + = 153 153 − 145 × 12 = 60 +4.36 = 64.36 22 Deciles : These are the values, which divide the total number of observation into 10 equal parts. These are 9 deciles D1, D2…D9. These are all called first decile, second decile… etc., 124 Deciles for Raw data or ungrouped data Example 25: Compute D5 for the data given below 5, 24, 36, 12, 20, 8 Solution : Arranging the given values in the increasing order 5, 8, 12, 20, 24, 36 th 5( n + 1) D5 = observation 10 th 5(6 + 1) = observation 10 = (3.5)th observation 1 = 3rd item + [ 4th item – 3rd item] 2 1 = 12 + [20 – 12] = 12+ 4 = 16 2 Deciles for Grouped data : Example 26: Calculate D3 and D7 for the data given below Class Interval 0-10 Frequency : Solution : 5 10-20 20-30 30-40 40-50 50-60 60-70 7 C.I 0-10 10-20 20-30 30-40 40-50 50-60 60-70 12 f 5 7 12 16 10 8 4 62 125 16 10 c.f 5 12 24 40 50 58 62 8 4 th 3N D3 item = item 10 th 3 × 62 = item 10 = (18.6)th item which lies in the interval 20-30 N 3 − m 10 ∴ D3 = l + ×c f 18.6 -12 = 20 + × 10 12 = 20 + 5.5 = 25.5 th 7× N D7 item = item 10 th 7 × 62 = item 10 th 434 th = item = (43.4) item 10 which lies in the interval(40-50) 7N 10 − m D7 = l + ×c f 43.4 − 40 = 40 + × 10 10 = 40 + 3.4 = 43.4 P...
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