Given information:
- Mean of 100 observed values is 50.

To find:
- Mean of resulting data if 7 is added to each observed value.

Approach:
To find the mean of the resulting data, we need to understand how adding a constant value to each observed value affects the mean.

Solution:

Step 1: Find the sum of the observed values
- Given that the mean of 100 observed values is 50.
- We know that the mean is calculated by summing all the observed values and dividing by the total number of values.
- Let's assume the sum of the observed values is 'S'.
- So we have: S/100 = 50

Step 2: Find the sum of the resulting data
- We are adding 7 to each observed value.
- This means that the sum of the resulting data will be the sum of the observed values plus 7 times the total number of values.
- Let's assume the sum of the resulting data is 'R'.
- So we have: R = S + 7*100

Step 3: Find the mean of the resulting data
- To find the mean, we need to divide the sum of the resulting data by the total number of values.
- The total number of values remains the same, which is 100.
- So the mean of the resulting data will be R/100.

Step 4: Substitute the value of S in equation R = S + 7*100
- From step 1, we know that S/100 = 50.
- Multiplying both sides of the equation by 100, we get: S = 5000.
- Substituting this value in the equation R = S + 7*100, we get: R = 5000 + 7*100.

Step 5: Calculate the mean of the resulting data
- Now we can calculate the mean of the resulting data by dividing R by 100.
- Let's calculate it: R/100 = (5000 + 7*100)/100 = (5000 + 700)/100 = 57.

Answer:
- The mean of the resulting data, when 7 is added to each observed value, is 57.