Find the average value and rms value of the numbers 1,2,3,-1,-2 and -3

Explanation

To find the average value and the root mean square (RMS) value of the numbers 1, 2, 3, -1, -2, and -3, we can follow these steps:

### Step 1: Calculate the Average Value
The average value (V_avg) is calculated using the formula:
\[ V_{avg} = \frac{\text{Sum of all values}}{\text{Total number of values}} \]

1. **List the values**: The numbers are 1, 2, 3, -1, -2, -3.
2. **Sum the values**:
\[ \text{Sum} = 1 + 2 + 3 + (-1) + (-2) + (-3) = 1 + 2 + 3 - 1 - 2 - 3 = 0 \]
3. **Count the total number of values**: There are 6 values.
4. **Calculate the average**:
\[ V_{avg} = \frac{0}{6} = 0 \]

### Step 2: Calculate the RMS Value
The RMS value is calculated using the formula:
\[ V_{rms} = \sqrt{\frac{\text{Sum of squares of all values}}{\text{Total number of values}}} \]

1. **Square each value**:
- \(1^2 = 1\)
- \(2^2 = 4\)
- \(3^2 = 9\)
- \((-1)^2 = 1\)
- \((-2)^2 = 4\)
- \((-3)^2 = 9\)

2. **Sum the squares**:
\[ \text{Sum of squares} = 1 + 4 + 9 + 1 + 4 + 9 = 28 \]

3. **Count the total number of values**: There are still 6 values.
4. **Calculate the RMS value**:
\[ V_{rms} = \sqrt{\frac{28}{6}} = \sqrt{\frac{14}{3}} \approx 2.16 \]

### Final Answers
- Average Value: \( V_{avg} = 0 \)
- RMS Value: \( V_{rms} \approx 2.16 \)