The mean of 15 observations is 32. Find the resulting mean if each observation is :
divided by 0.5

Answer

To find the resulting mean when each observation is divided by 0.5, follow these steps:

### Step 1: Calculate the sum of the original observations
Given that the mean of 15 observations is 32, we can calculate the total sum of these observations.

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

So, we can rearrange this to find the sum:

\[ \text{Sum of observations} = \text{Mean} \times \text{Number of observations} = 32 \times 15 \]

Calculating this gives:

\[ \text{Sum of observations} = 480 \]

### Step 2: Determine the new observations after division
When each observation \( x_i \) is divided by 0.5, the new observation becomes:

\[ \frac{x_i}{0.5} = 2x_i \]

This means each observation is multiplied by 2.

### Step 3: Calculate the new sum of observations
The new sum of the observations after this transformation will be:

\[ \text{New Sum} = 2x_1 + 2x_2 + \ldots + 2x_{15} = 2(x_1 + x_2 + \ldots + x_{15}) \]

Substituting the sum we found in Step 1:

\[ \text{New Sum} = 2 \times 480 = 960 \]

### Step 4: Calculate the new mean
Now, we can find the new mean using the new sum of observations:

\[ \text{New Mean} = \frac{\text{New Sum}}{\text{Number of observations}} = \frac{960}{15} \]

Calculating this gives:

\[ \text{New Mean} = 64 \]

### Final Answer
The resulting mean after dividing each observation by 0.5 is **64**.

---