The mean and standard deviation of 6 observations are 8 and 4 respectively . If each observation is multiplied by 2, find the new mean and new standard deviation of the resulting observation.

Answer

To solve the problem step by step, we will find the new mean and new standard deviation after multiplying each observation by 2.

### Step 1: Understand the Given Information
We are given:
- Mean (μ) of 6 observations = 8
- Standard deviation (σ) of 6 observations = 4
- Number of observations (n) = 6

### Step 2: Calculate the New Mean
When each observation is multiplied by a constant (in this case, 2), the new mean is also multiplied by that constant.

\[ \text{New Mean} = 2 \times \text{Old Mean} \]
\[ \text{New Mean} = 2 \times 8 = 16 \]

### Step 3: Calculate the New Standard Deviation
Similarly, when each observation is multiplied by a constant, the new standard deviation is multiplied by the absolute value of that constant.

\[ \text{New Standard Deviation} = 2 \times \text{Old Standard Deviation} \]
\[ \text{New Standard Deviation} = 2 \times 4 = 8 \]

### Final Answer
- New Mean = 16
- New Standard Deviation = 8