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JEE Main202623 January 2026Evening ShiftMathematicsStatisticsActual

If the mean and the variance of the data ( array |c|c|c|c|c| Class & 4 - 8 & 8 - 12 & 12 - 16 & 16 - 20 Frequency & 3 & & 4 & 7 array ) are and 19 respectively, then the value of + is

Options

  1. A21
  2. B19
  3. C20
  4. D18

Correct answer

B. 19

Step-by-step solution

Class midpoints: 6, 10, 14, 18 . Frequencies: 3, , 4, 7 . N = 14 + . Mean = 200 + 10 14 + . f_i x_i^2 = 3(36) + 100 + 4(196) + 7(324) = 3160 + 100 . Variance: 19 = 3160+100 N - ^2 . Let u = 14+ : 19u^2 = u(1760+100u) - (60+10u)^2 19u^2 - 560u + 3600 = 0 . u = 560 200 38 , so u = 20 = 6 . = 260 20 = 13 . Hence + = 6 + 13 = 19 .

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