Multiple choice

The following observations are arranged in ascending order: $26, 29, 42, 53, x, x+2, 70, 75, 82, 93$ If the median is $65,$ find the value of $x$.

  1. $62$
  2. $64$
  3. $65$
  4. $68$
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B Correct answer
Explanation

There are 10 observations. The median is the average of the 5th and 6th terms: (x + x + 2) / 2 = 65. Solving this, 2x + 2 = 130, so 2x = 128, x = 64.

AI explanation

Because there are 10 observations, the median is the average of the 5th and 6th terms. The 5th term is x and the 6th term is x plus 2. Set their average to 65 to get x plus 1 equals 65. Solving this gives x equals 64. The value of x is 64.

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