The mean of 10 observations is 13. Two more observations are included and the new mean becomes 14. The mean of two new observations is
A. 19
B. 18
C. 17
D. 16

Options

A. A
B. D
C. B
D. C

Answer

To solve the problem step by step, we will use the formula for the mean and perform calculations based on the information provided.

### Step-by-Step Solution:

1. **Understand the Given Information**:
- The mean of 10 observations is 13.
- Two more observations are added, and the new mean becomes 14.

2. **Calculate the Sum of the First 10 Observations**:
- The formula for the mean is:
\[ \text{Mean} = \frac{\text{Sum of observations}}{\text{Number of observations}} \]
- For the first 10 observations:
\[ 13 = \frac{\text{Sum of 10 observations}}{10} \]
- Therefore, the sum of the first 10 observations is:
\[ \text{Sum of 10 observations} = 13 \times 10 = 130 \]

3. **Calculate the Sum of All 12 Observations**:
- After adding 2 more observations, the new mean is 14:
\[ 14 = \frac{\text{Sum of 12 observations}}{12} \]
- Thus, the sum of all 12 observations is:
\[ \text{Sum of 12 observations} = 14 \times 12 = 168 \]

4. **Find the Sum of the Two New Observations**:
- The sum of the two new observations can be calculated by subtracting the sum of the first 10 observations from the sum of all 12 observations:
\[ \text{Sum of 2 new observations} = \text{Sum of 12 observations} - \text{Sum of 10 observations} \]
- Plugging in the values:
\[ \text{Sum of 2 new observations} = 168 - 130 = 38 \]

5. **Calculate the Mean of the Two New Observations**:
- The mean of the two new observations is given by:
\[ \text{Mean of 2 new observations} = \frac{\text{Sum of 2 new observations}}{2} \]
- Therefore:
\[ \text{Mean of 2 new observations} = \frac{38}{2} = 19 \]

6. **Conclusion**:
- The mean of the two new observations is 19.

### Final Answer:
- The mean of the two new observations is **19** (Option A).