Multiple choice

The average of $6$ observations is $12$. A new seventh observation is included and the new average is decreased by $1$. The seventh observation is

  1. $1$
  2. $3$
  3. $5$
  4. $6$
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C Correct answer
Explanation

Sum of 6 observations = 6 * 12 = 72. Sum of 7 observations = 7 * (12-1) = 7 * 11 = 77. The seventh observation is 77 - 72 = 5.

AI explanation

The initial sum of the 6 observations is 6 multiplied by 12, which equals 72. The new average after including the seventh observation is 12 minus 1, giving 11, so the new total sum for 7 observations is 7 multiplied by 11 (77). The value of the seventh observation is the difference between the new sum and the initial sum. Therefore, 77 minus 72 equals 5.

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