Mean of 15 observations is 200. If one observation is excluded, the mean of remaining observations is 198.Find the value of the excluded observation.

Answer

To solve the problem step by step, we will follow the information provided in the question and use the formulas for mean.

### Step 1: Calculate the total sum of the 15 observations.
Given that the mean of 15 observations is 200, we can find the total sum of these observations using the formula:

\[ \text{Sum} = \text{Mean} \times \text{Number of Observations} \]

Substituting the values:

\[ \text{Sum} = 200 \times 15 = 3000 \]

### Step 2: Calculate the total sum of the remaining 14 observations.
When one observation is excluded, the mean of the remaining 14 observations is 198. We can find the total sum of these 14 observations using the same formula:

\[ \text{New Sum} = \text{New Mean} \times \text{New Number of Observations} \]

Substituting the values:

\[ \text{New Sum} = 198 \times 14 = 2772 \]

### Step 3: Find the value of the excluded observation.
Let \( X \) be the excluded observation. The relationship between the old sum, new sum, and the excluded observation can be expressed as:

\[ \text{Old Sum} = \text{New Sum} + X \]

Substituting the known sums:

\[ 3000 = 2772 + X \]

Now, we can solve for \( X \):

\[ X = 3000 - 2772 = 228 \]

### Conclusion:
The value of the excluded observation is \( 228 \).

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