The mean of 16 numbers is 8. If 2 is added to every number, what will be the new mean?

Answer

To solve the problem step by step, we will determine the new mean after adding 2 to each of the 16 numbers.

### Step 1: Understand the given information
We know that the mean of 16 numbers is 8.

### Step 2: Calculate the total 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 8 and the number of observations is 16, we can set up the equation:
\[ 8 = \frac{\text{Sum of all observations}}{16} \]
To find the sum of all observations, we can multiply both sides by 16:
\[ \text{Sum of all observations} = 8 \times 16 = 128 \]

### Step 3: Determine the new sum after adding 2 to each number
If we add 2 to each of the 16 numbers, the new sum will be:
\[ \text{New Sum} = \text{Original Sum} + (2 \times \text{Number of observations}) \]
Substituting the values we have:
\[ \text{New Sum} = 128 + (2 \times 16) = 128 + 32 = 160 \]

### Step 4: Calculate the new mean
Now, we can calculate the new mean using the new sum:
\[ \text{New Mean} = \frac{\text{New Sum}}{\text{Number of observations}} = \frac{160}{16} = 10 \]

### Conclusion
The new mean after adding 2 to each number is **10**.

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