The mean of the remaining observations after excluding two values can be calculated as follows:

Given:
- Number of observations: 50
- Mean of the observations: 36
- Two observations to be excluded: 30 and 42

Step 1: Calculate the sum of all the observations.
To find the sum of all the observations, we multiply the mean by the total number of observations:
Sum of all observations = Mean * Number of observations
= 36 * 50
= 1800

Step 2: Subtract the values of the excluded observations from the sum.
We need to subtract the values of the two excluded observations, 30 and 42, from the sum calculated in the previous step:
Sum of remaining observations = Sum of all observations - Sum of excluded observations
= 1800 - (30 + 42)
= 1800 - 72
= 1728

Step 3: Calculate the new mean.
To find the mean of the remaining observations, we divide the sum of the remaining observations by the number of remaining observations:
New mean = Sum of remaining observations / Number of remaining observations
= 1728 / (50 - 2)
= 1728 / 48
= 36

Explanation:
The mean is a measure of central tendency that represents the average value of a set of observations. In this case, the mean of the 50 observations is given as 36. To find the mean of the remaining observations after excluding two values (30 and 42), we follow the steps outlined above.

Firstly, we calculate the sum of all the observations by multiplying the mean by the total number of observations. Then, we subtract the values of the excluded observations from the sum to find the sum of the remaining observations.

Finally, we calculate the new mean by dividing the sum of the remaining observations by the number of remaining observations. In this case, the new mean is also found to be 36.

This process ensures that the excluded observations do not influence the calculation of the mean of the remaining observations.