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JEE Main202122 Jul 2021Morning ShiftMathematicsStatisticsActual

Consider the following frequency distribution: Class: 0 - 6 6 - 12 12 - 18 18 - 24 24 - 30 Frequency: a b 12 9 5 If mean = 309 22 and median = 14 , then the value ( a - b ) 2 is equal to

Correct answer

0

Step-by-step solution

Class Frequency Mid-point x i f i x i 0 - 6 a 0 + 6 2 = 3 3 a 6 - 12 b 6 + 12 2 = 9 9 b 12 - 18 12 12 + 18 2 = 15 180 18 - 24 9 18 + 24 2 = 21 189 24 - 30 5 24 + 30 2 = 27 135 N = 26 + a + b 504 + 3 a + 9 b We know that, mean = ∑ f i x i ∑ f i Given, mean = 309 22 ⇒ 3 a + 9   b + 180 + 189 + 135 a + b + 26 = 309 22 ⇒ 504 + 3 a + 9   b a + b + 26 = 309 22 ⇒ 66 a + 198   b + 11088 = 309 a + 309   b + 8034 ⇒ 243 a + 111   b = 3054 ⇒ 81 a + 37 b = 1018

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