The mean of a certain number of observations is 35. What is the new value of the mean if each observation is :
Multiplied by 2.

Answer

To find the new mean when each observation is multiplied by 2, we can follow these steps:

### Step 1: Understand the given information
The mean of a certain number of observations is given as 35.

### Step 2: Let’s denote the number of observations
Let the number of observations be \( n \).

### Step 3: Calculate the sum of the observations
The formula for the mean is:
\[ \text{Mean} = \frac{\text{Sum of observations}}{\text{Total number of observations}} \]
From the information given, we can express the sum of the observations as:
\[ \text{Sum of observations} = \text{Mean} \times n = 35 \times n = 35n \]

### Step 4: Determine the new sum when each observation is multiplied by 2
If each observation is multiplied by 2, the new sum of the observations will be:
\[ \text{New sum} = 2 \times (\text{Sum of observations}) = 2 \times 35n = 70n \]

### Step 5: Calculate the new mean
Now, we can find the new mean using the new sum:
\[ \text{New Mean} = \frac{\text{New sum}}{\text{Total number of observations}} = \frac{70n}{n} \]
Since \( n \) cancels out, we have:
\[ \text{New Mean} = 70 \]

### Final Answer:
The new value of the mean when each observation is multiplied by 2 is **70**.

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