If the median of the observations 2, 3, 5, 6, x, 8, 9, is 6 then x CANNOT be equal to: 

The correct answer is 1. 
Key Points 

Given the observations 2, 3, 5, 6, x, 8, 9, to determine the median, we arrange the observations in ascending order: 2, 3, 5, 6, x, 8, 9. 
Since the number of observations is odd, the median is the middle value in the ordered list. In this case, the fourth observation, which is 6, represents the median.

• To identify the values that x cannot be equal to, we need to consider the possible positions of x in the ordered list. 
  • If x is less than 6, it would be positioned to the left of 6 in the list. In such a case, the median would be greater than 6, as the middle value would shift to a higher number. Therefore, x cannot be less than 6.
  • If x is greater than 6, it would be positioned to the right of 6 in the ordered list. In this case, the median would still be 6 since it represents the middle value. Therefore, x can be greater than 6.
  • If x equals 6, it would coincide with the median, as it represents the middle value in the ordered list. Therefore, x can be equal to 6.
     

Hence, considering the given information that the median is known to be 6, it can be concluded that x cannot be equal to 1, as it is less than 6.