The mean of 12 observations is 15. One more observation is included and the new mean becomes 16, The 13th observation is
A. 20
B. 24
C. 26
D. 28

Options

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

Answer

To solve the problem step by step, we will use the information given about the mean of the observations.

### Step 1: Calculate the sum of the first 12 observations.
The mean of the first 12 observations is given as 15. The formula for the mean is:

\[ \text{Mean} = \frac{\text{Sum of observations}}{\text{Number of observations}} \]

Using this formula, we can find the sum of the first 12 observations:

\[ \text{Sum of 12 observations} = \text{Mean} \times \text{Number of observations} = 15 \times 12 = 180 \]

### Step 2: Calculate the sum of the 13 observations.
When one more observation is added, the new mean becomes 16. Now we have 13 observations. We can find the sum of these 13 observations using the same formula:

\[ \text{Sum of 13 observations} = \text{Mean} \times \text{Number of observations} = 16 \times 13 = 208 \]

### Step 3: Find the 13th observation.
Now, we need to find the value of the 13th observation. We can do this by subtracting the sum of the first 12 observations from the sum of the 13 observations:

\[ \text{13th observation} = \text{Sum of 13 observations} - \text{Sum of 12 observations} = 208 - 180 = 28 \]

### Conclusion
The 13th observation is 28.

### Answer
D. 28

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