The mean of 12 numbers is 40. if each number is divided by 8, what will be the mean of the new numbers ?

Answer

To solve the problem step by step, let's break it down:

### Step 1: Understand the Mean
The mean (average) of a set of numbers is calculated by dividing the sum of all the numbers by the count of the numbers. In this case, we know that the mean of 12 numbers is 40.

### Step 2: Calculate the Total Sum of the Original Numbers
To find the total sum of the original 12 numbers, we can use the formula:
\[ \text{Mean} = \frac{\text{Sum of numbers}}{\text{Count of numbers}} \]
Given that the mean is 40 and the count is 12, we can rearrange the formula to find the sum:
\[ \text{Sum of numbers} = \text{Mean} \times \text{Count} = 40 \times 12 = 480 \]

### Step 3: Understand the Transformation
Now, we need to find the mean of the new numbers, which are obtained by dividing each of the original numbers by 8.

### Step 4: Calculate the New Mean
When each number is divided by 8, the new mean can be calculated as:
\[ \text{New Mean} = \frac{\text{Original Mean}}{8} \]
Substituting the original mean:
\[ \text{New Mean} = \frac{40}{8} = 5 \]

### Final Answer
Thus, the mean of the new numbers is **5**.

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