The mean of 14 observations in 11 . One more observation in included and the new mean becoems 12 . The `15^(th)` observation is
A. 20
B. 24
C. 26
D. 28

Options

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

Answer

To solve the problem step by step, we need to find the 15th observation based on the given information about the mean of the observations.

### Step 1: Calculate the sum of the first 14 observations.
The mean of the first 14 observations is given as 11. We can use the formula for the mean:

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

Let \( S \) be the sum of the first 14 observations. Therefore, we can write:

\[ 11 = \frac{S}{14} \]

Multiplying both sides by 14 gives:

\[ S = 11 \times 14 = 154 \]

### Step 2: Calculate the new sum when the 15th observation is included.
When one more observation is added, the new mean becomes 12. Now, we have 15 observations. Let the 15th observation be \( x \). The new sum of all 15 observations can be expressed as:

\[ \text{New Mean} = \frac{S + x}{15} \]

Substituting the new mean:

\[ 12 = \frac{154 + x}{15} \]

### Step 3: Solve for the 15th observation.
To find \( x \), we can multiply both sides by 15:

\[ 12 \times 15 = 154 + x \]

Calculating the left side:

\[ 180 = 154 + x \]

Now, isolate \( x \):

\[ x = 180 - 154 = 26 \]

### Conclusion
The 15th observation is \( 26 \).

### Final Answer
The 15th observation is **C. 26**.