Given:
Mean of 25 observations = 36
Mean of first 13 observations = 32
Mean of last 13 observations = 39

We need to find the 13th observation.

Mean of 25 observations
The mean of 25 observations is given as 36. This means that if we add up all the observations and divide the sum by 25, we will get the value 36.

Mean of first 13 observations
The mean of the first 13 observations is given as 32. This means that if we add up the values of the first 13 observations and divide the sum by 13, we will get the value 32.

Mean of last 13 observations
Similarly, the mean of the last 13 observations is given as 39. This means that if we add up the values of the last 13 observations and divide the sum by 13, we will get the value 39.

Finding the sum of all 25 observations
To find the sum of all 25 observations, we can multiply the mean (36) by the total number of observations (25). So, the sum of all 25 observations is 36 * 25 = 900.

Finding the sum of the first 13 observations
To find the sum of the first 13 observations, we can multiply the mean (32) by the number of observations (13). So, the sum of the first 13 observations is 32 * 13 = 416.

Finding the sum of the last 13 observations
Similarly, to find the sum of the last 13 observations, we can multiply the mean (39) by the number of observations (13). So, the sum of the last 13 observations is 39 * 13 = 507.

Finding the sum of the remaining 12 observations
To find the sum of the remaining 12 observations (excluding the first and last 13 observations), we can subtract the sum of the first 13 observations (416) and the sum of the last 13 observations (507) from the sum of all 25 observations (900).
So, the sum of the remaining 12 observations is 900 - 416 - 507 = -23.

Finding the value of the 13th observation
To find the value of the 13th observation, we can subtract the sum of the remaining 12 observations (-23) from the sum of the first 13 observations (416).
So, the value of the 13th observation is 416 - (-23) = 439.

Therefore, the 13th observation is 439, which does not match any of the given options (a, b, c, or d).