The mean of 15 observations is 32. Find the resulting mean if each observation is :
increased by 3

Answer

To find the new mean when each observation is increased by 3, we can follow these steps:

### Step 1: Calculate the sum of the original observations
Given that the mean of 15 observations is 32, we can find the sum of these observations using the formula for mean:

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

Let the sum of the observations be \( S \). Therefore, we have:

\[ 32 = \frac{S}{15} \]

To find \( S \), we can rearrange the equation:

\[ S = 32 \times 15 \]

Calculating this gives:

\[ S = 480 \]

### Step 2: Calculate the new sum after increasing each observation by 3
If each of the 15 observations is increased by 3, the new sum \( S' \) can be calculated as follows:

\[ S' = S + (3 \times 15) \]

Substituting the value of \( S \):

\[ S' = 480 + (3 \times 15) \]

Calculating \( 3 \times 15 \):

\[ 3 \times 15 = 45 \]

Now substituting back:

\[ S' = 480 + 45 = 525 \]

### Step 3: Calculate the new mean
The new mean \( \text{Mean}' \) can be calculated using the new sum \( S' \) and the number of observations (which remains 15):

\[ \text{Mean}' = \frac{S'}{15} \]

Substituting the value of \( S' \):

\[ \text{Mean}' = \frac{525}{15} \]

Calculating this gives:

\[ \text{Mean}' = 35 \]

### Final Answer
The resulting mean after increasing each observation by 3 is **35**.

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