Find the mean of the following data: 18, 33, 30, 21 and 13.
Also, find the sum of deviations of this data from the mean.

Answer

To solve the problem, we will follow these steps:

### Step 1: Calculate the Mean
The mean (average) of a set of numbers is calculated by dividing the sum of the numbers by the total count of the numbers.

1. **List the numbers**: 18, 33, 30, 21, 13
2. **Sum the numbers**:
\[ 18 + 33 + 30 + 21 + 13 \]
- First, add 18 and 33:
\[ 18 + 33 = 51 \]
- Next, add 30:
\[ 51 + 30 = 81 \]
- Then, add 21:
\[ 81 + 21 = 102 \]
- Finally, add 13:
\[ 102 + 13 = 115 \]
So, the sum of the numbers is 115.

3. **Count the numbers**: There are 5 numbers in total.

4. **Calculate the mean**:
\[ \text{Mean} = \frac{\text{Sum of observations}}{\text{Number of observations}} = \frac{115}{5} = 23 \]

### Step 2: Calculate the Sum of Deviations from the Mean
The sum of deviations from the mean is calculated by finding the absolute difference between each number and the mean, and then summing these differences.

1. **Calculate each deviation**:
- For 18:
\[ |18 - 23| = | -5 | = 5 \]
- For 33:
\[ |33 - 23| = |10| = 10 \]
- For 30:
\[ |30 - 23| = |7| = 7 \]
- For 21:
\[ |21 - 23| = |-2| = 2 \]
- For 13:
\[ |13 - 23| = |-10| = 10 \]

2. **Sum the deviations**:
\[ 5 + 10 + 7 + 2 + 10 = 34 \]

### Final Answers:
- The mean of the data is **23**.
- The sum of deviations from the mean is **34**.

---