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Statistics · Question 20

JEE Main 2025 (Online) 2nd April Evening ShiftMCQEasy📈 Topic in 45% papers+4−1
1

If the mean and the variance of 6, 4, a, 8, b, 12, 10, 13 are 9 and 9.25 respectively, then a + b + ab is equal to :

  1. 103
  2. 106
  3. 100
  4. 105

Answer

(1) 103

Solution

Number of observations = 8

Mean: 6 + 4 + a + 8 + b + 12 + 10 + 138 = 9

53 + a + b = 72 a + b = 19

Variance: xi28 - 92 = 9.25

xi2 = 8 90.25 = 722

36 + 16 + 64 + 144 + 100 + 169 + a2 + b2 = 722

a2 + b2 = 722 - 529 = 193

2ab = (a + b)2 - (a2 + b2) = 361 - 193 = 168 ab = 84

a + b + ab = 19 + 84 = 103

Answer: (1)

JEE Main 2025 (Online) 2nd April Evening Shift

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2

Let x1, x2, , x10 be ten observations such that i=110(xi - 2) = 30, i=110(xi - )2 = 98, > 2, and their variance is 45. If and 2 are respectively the mean and the variance of 2(x1 - 1) + 4 , 2(x2 - 1) + 4 , , 2(x10 - 1) + 4 , then 2 is equal to :

  1. 100
  2. 90
  3. 120
  4. 110
JEE Main 2025 (Online) 29th January Morning Shift

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