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      Question

      The marks (out of 50) of 5 students are: 10, 14, 18, x,

      26. The mean is 18. Find x and the standard deviation.
      A 7√3 Correct Answer Incorrect Answer
      B 3√2 Correct Answer Incorrect Answer
      C 4√2 Correct Answer Incorrect Answer
      D 2√2 Correct Answer Incorrect Answer

      Solution

      Mean = 18 β‡’ total sum = 5 Γ— 18 = 90 Known sum = 10 + 14 + 18 + 26 = 68 So x = 90 βˆ’ 68 = 22 Data: 10, 14, 18, 22, 26; mean = 18 Deviations from mean: 10 βˆ’ 18 = βˆ’8 14 βˆ’ 18 = βˆ’4 18 βˆ’ 18 = 0 22 βˆ’ 18 = 4 26 βˆ’ 18 = 8 Squares: 64, 16, 0, 16, 64 Sum of squares = 160 Standard deviation (population) = √(Ξ£(dΒ²)/n) = √(160/5) = √32 = 4√2.

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