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 will follow the logic provided in the video transcript.

### Step 1: Calculate the sum of the five numbers
We know that the mean of 5 numbers is 18. The formula for the mean is:

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

Using this formula, we can express the sum of the five numbers (let's call it \( S \)) as follows:

\[ \frac{S}{5} = 18 \]

To find \( S \), we can multiply both sides by 5:

\[ S = 18 \times 5 = 90 \]

### Step 2: Set up the equation for the remaining numbers
Let the excluded number be \( x \). When we exclude this number, the sum of the remaining four numbers will be:

\[ S - x = 90 - x \]

The mean of these four numbers is given to be 16. Therefore, we can set up the following equation:

\[ \frac{90 - x}{4} = 16 \]

### Step 3: Solve for the excluded number \( x \)
To eliminate the fraction, we can multiply both sides of the equation by 4:

\[ 90 - x = 16 \times 4 \]

Calculating the right side:

\[ 90 - x = 64 \]

Now, we can isolate \( x \) by rearranging the equation:

\[ -x = 64 - 90 \]
\[ -x = -26 \]

Multiplying both sides by -1 gives:

\[ x = 26 \]

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

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