Mean of 18 numbers is 10. If 2 is multiplied to every number, what will be the new mean?

Answer

To find the new mean after multiplying each of the 18 numbers by 2, we can follow these steps:

### Step 1: Understand the given information
We know that the mean of 18 numbers is 10.

### Step 2: Calculate the sum of the original numbers
The mean is calculated using the formula:
\[ \text{Mean} = \frac{\text{Sum of all observations}}{\text{Number of observations}} \]
Given that the mean is 10 and there are 18 numbers, we can express this as:
\[ 10 = \frac{x_1 + x_2 + x_3 + \ldots + x_{18}}{18} \]
To find the sum of the numbers, we multiply both sides by 18:
\[ x_1 + x_2 + x_3 + \ldots + x_{18} = 10 \times 18 = 180 \]

### Step 3: Multiply each number by 2
When we multiply each of the original numbers by 2, the new numbers will be:
\[ 2x_1, 2x_2, 2x_3, \ldots, 2x_{18} \]

### Step 4: Calculate the sum of the new numbers
The sum of the new numbers can be calculated as:
\[ 2x_1 + 2x_2 + 2x_3 + \ldots + 2x_{18} = 2(x_1 + x_2 + x_3 + \ldots + x_{18}) = 2 \times 180 = 360 \]

### Step 5: Calculate the new mean
Now, we can find the new mean using the formula for mean:
\[ \text{New Mean} = \frac{\text{Sum of new observations}}{\text{Number of observations}} = \frac{360}{18} \]
Calculating this gives:
\[ \text{New Mean} = 20 \]

### Conclusion
The new mean after multiplying each number by 2 is **20**.

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