The mean of 5 numbers is 18. If one number is excluded, the mean of remaining numbers becomes 16. Find the excluded number.

Answer

To solve the problem step by step, we can follow the outlined approach below:

### Step 1: Understand the given information
We know that the mean of 5 numbers is 18. This means that the total sum of these 5 numbers can be calculated.

### Step 2: Calculate the total sum of the 5 numbers
The mean (average) is calculated as:
\[ \text{Mean} = \frac{\text{Sum of all numbers}}{\text{Number of observations}} \]
Given that the mean is 18 and the number of observations is 5, we can set up the equation:
\[ 18 = \frac{\text{Sum of 5 numbers}}{5} \]
Multiplying both sides by 5 gives:
\[ \text{Sum of 5 numbers} = 18 \times 5 = 90 \]

### Step 3: Calculate the total sum of the remaining 4 numbers
When one number is excluded, the mean of the remaining 4 numbers becomes 16. We can calculate the total sum of these 4 numbers using the same mean formula:
\[ 16 = \frac{\text{Sum of remaining 4 numbers}}{4} \]
Multiplying both sides by 4 gives:
\[ \text{Sum of remaining 4 numbers} = 16 \times 4 = 64 \]

### Step 4: Find the excluded number
The excluded number can be found by subtracting the sum of the remaining 4 numbers from the total sum of the original 5 numbers:
\[ \text{Excluded number} = \text{Sum of 5 numbers} - \text{Sum of remaining 4 numbers} \]
Substituting the values we calculated:
\[ \text{Excluded number} = 90 - 64 = 26 \]

### Conclusion
The excluded number is **26**.

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