The mean of five numbers is 30. If one number is excluded, their mean becomes 28. The excluded number is.
(a)28
(b)30
(c)35
(d)38

Options

A. 28
B. 30
C. 35
D. 38

Answer

To find the excluded number from the given problem, we can follow these steps:

### Step 1: Calculate the sum of the five numbers
We know the mean of five numbers is 30. The formula for the mean is:

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

From this, we can rearrange the formula to find the sum of the observations:

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

Substituting the values we have:

\[ \text{Sum of observations} = 30 \times 5 = 150 \]

### Step 2: Calculate the sum of the four remaining numbers
When one number is excluded, the mean of the remaining four numbers becomes 28. We can use the same formula to find the sum of these four numbers:

\[ \text{Sum of 4 numbers} = \text{Mean} \times \text{Number of observations} = 28 \times 4 = 112 \]

### Step 3: Find the excluded number
The excluded number can be found by subtracting the sum of the four numbers from the sum of the five numbers:

\[ \text{Excluded number} = \text{Sum of 5 numbers} - \text{Sum of 4 numbers} = 150 - 112 = 38 \]

Thus, the excluded number is **38**.

### Final Answer:
The excluded number is **(d) 38**.

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