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# 2 median can be calculated in case of distribution

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Unformatted text preview: d value other than any value in the series. 3. It is not suitable for further mathematical treatment except its use in mean deviation. 4. It is not taken into account all the observations. Quartiles : The quartiles divide the distribution in four parts. There are three quartiles. The second quartile divides the distribution into two halves and therefore is the same as the median. The first (lower) quartile (Q1) marks off the first one-fourth, the third (upper) quartile (Q3) marks off the three-fourth. Raw or ungrouped data: First arrange the given data in the increasing order and use the formula for Q1 and Q3 then quartile deviation, Q.D is given by Q 3 - Q1 Q.D = 2 n + 1 th n + 1 th Where Q1= item and Q3 = 3 item 4 4 Example 22 : Compute quartiles for the data given below 25,18,30, 8, 15, 5, 10, 35, 40, 45 Solution : 5, 8, 10, 15, 18,25, 30,35,40, 45 120 n + 1 th Q1 = item 4 10 + 1 th = item 4 = (2.75)th item 3 = 2nd item + (3rd item-2nd item) 4 3 = 8+ (10-8) 4 3 = 8+ ×2 4 = 8 + 1.5 = 9.5 th n +1 Q3 = 3 item 4 = 3 × (2.75)th item = (8.25)th item 1 th = 8th item + [9 item-8th item] 4 1 = 35 + [40-35] 4 = 35+1.25=36.25 Discrete Series : Step1: Find cumulative frequencies. N + 1 Step2: Find 4 Step3: See in the cumulative frequencies , the value just greater N + 1 than ,then the corresponding value of x is Q1 4 N + 1 Step4: Find 3 4 121 Step5: See in the cumulative frequencies, the value just greater N + 1 than 3 ,then the corresponding value of x is Q3 4 Example 23: Compute quartiles for the data given bellow. X f 5 4 8 3 12 2 15 4 19 5 24 2 30 4 Solution: x 5 8 12 15 19 24 30 Total th f 4 3 2 4 5 2 4 24 N +1 24 + 1 Q1 = item = 4 4 c.f 4 7 9 13 18 20 24 25 = = 6.25th item 4 th N +1 24 + 1 th Q3 = 3 =18.75 item ∴Q1= 8; Q3=24 item = 3 4 4 Continuous series : Step1: Find cumulative frequencies N Step2: Find 4 Step3: See in the cumulative frequencies, the value just greater N than , then the corresponding class interval is called 4 first quartile class. 122 N Step4: Find 3 See in the cumulative frequencies the value 4 N just greater than 3 then the corresponding class int...
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