The mean of 10 observations is 5. If 2 is added to each observation and then multiplied by 3, then what will be the new mean?

Options

A. 5
B. 7
C. 15
D. 21

Explanation

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

### Step 1: Calculate the total of the original observations
Given that the mean of 10 observations is 5, we can find the total of these observations.

\[ \text{Total} = \text{Mean} \times \text{Number of Observations} = 5 \times 10 = 50 \]

### Step 2: Add 2 to each observation
When we add 2 to each of the 10 observations, the total increase in the sum of the observations will be:

\[ \text{Total after adding 2} = \text{Original Total} + (2 \times 10) = 50 + 20 = 70 \]

### Step 3: Multiply each observation by 3
Next, we multiply each observation by 3. This means we multiply the new total by 3:

\[ \text{Total after multiplying by 3} = 70 \times 3 = 210 \]

### Step 4: Calculate the new mean
Now, we can find the new mean by dividing the new total by the number of observations:

\[ \text{New Mean} = \frac{\text{Total after multiplying by 3}}{\text{Number of Observations}} = \frac{210}{10} = 21 \]

### Conclusion
The new mean after adding 2 to each observation and then multiplying by 3 is **21**.

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