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JEE Main202330 Jan 2023Morning ShiftMathematicsStatisticsActual

The mean and variance of 7 observations are 8 and 16 respectively. If one observation 14 is omitted, a and b are respectively mean and variance of remaining 6 observation, then a + 3 b - 5 is equal to ________

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Step-by-step solution

Given, Mean and variance of 7 observation is given as 8   &   16 respectively, So using the formula of mean we get, x ¯ = S 7 ⇒ S = 8 × 7 = 56 Now if we remove 14 sum will be S = 56 - 14 = 42 and new mean will be a = 42 6 = 7 Now using the formula of variance we get, ∑ i = 1 6 x i 2 + 14 2 7 - x ¯ 2 = 16 ⇒ ∑ i = 1 6 x i 2 + 14 2 7 - 8 2 = 16 ⇒ ∑ i = 1 6 x i 2 + 14 2 7 = 80 ⇒ ∑ i = 1 6 x i 2 + 14 2 = 560 ⇒ ∑ i = 1 6 x i = 364 No

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