If the algebraic sum of deviations of 20 observation from 30 is 20, then the mean of observation is :

Explanation

To find the mean of the observations given that the algebraic sum of deviations of 20 observations from 30 is 20, we can follow these steps:

### Step 1: Understand the Problem
We have 20 observations, and we need to find their mean. The deviations of these observations from a reference point (which is 30) sum up to 20.

### Step 2: Define the Observations
Let the observations be \( A_1, A_2, A_3, \ldots, A_{20} \). The deviation of each observation \( A_i \) from 30 can be defined as:
\[ x_i = A_i - 30 \]
where \( i = 1, 2, \ldots, 20 \).

### Step 3: Set Up the Equation for Deviations
According to the problem, the algebraic sum of deviations is given by:
\[ x_1 + x_2 + x_3 + \ldots + x_{20} = 20 \]

### Step 4: Express Each Observation in Terms of Deviations
We can express each observation in terms of the deviations:
\[ A_i = x_i + 30 \]
Thus, the sum of all observations can be written as:
\[ A_1 + A_2 + A_3 + \ldots + A_{20} = (x_1 + 30) + (x_2 + 30) + (x_3 + 30) + \ldots + (x_{20} + 30) \]

### Step 5: Simplify the Sum of Observations
This can be simplified to:
\[ A_1 + A_2 + A_3 + \ldots + A_{20} = (x_1 + x_2 + x_3 + \ldots + x_{20}) + 30 \times 20 \]
\[ = (x_1 + x_2 + x_3 + \ldots + x_{20}) + 600 \]

### Step 6: Substitute the Sum of Deviations
Now, substituting the sum of deviations (which is 20):
\[ A_1 + A_2 + A_3 + \ldots + A_{20} = 20 + 600 = 620 \]

### Step 7: Calculate the Mean
The mean \( \bar{A} \) of the observations is given by:
\[ \bar{A} = \frac{A_1 + A_2 + A_3 + \ldots + A_{20}}{20} \]
Substituting the sum we found:
\[ \bar{A} = \frac{620}{20} = 31 \]

### Conclusion
Thus, the mean of the observations is:
\[ \boxed{31} \]