Let's analyze the given data set and calculate the variance step-by-step.
Given data:
```
[value1, value2, value3, value4, value5]
```
To find the variance, we need the mean ([tex]\(\mu\)[/tex]) of the data set and then utilize the given formula for variance ([tex]\(\sigma^2\)[/tex]):
[tex]\(\sigma^2 = \frac{(x_1 - \mu)^2 + (x_2 - \mu)^2 + \ldots + (x_N - \mu)^2}{N}\)[/tex]
### Step-by-Step Calculation:
1. Calculate the Mean ([tex]\(\mu\)[/tex]):
- Let [tex]\( N \)[/tex] be the number of values in the data set. In this case, [tex]\( N = 5 \)[/tex].
- The mean ([tex]\(\mu\)[/tex]) is calculated using:
[tex]\[
\mu = \frac{value1 + value2 + value3 + value4 + value5}{N}
\][/tex]
2. Calculate each squared difference from the mean:
- Compute [tex]\((value1 - \mu)^2\)[/tex]
- Compute [tex]\((value2 - \mu)^2\)[/tex]
- Compute [tex]\((value3 - \mu)^2\)[/tex]
- Compute [tex]\((value4 - \mu)^2\)[/tex]
- Compute [tex]\((value5 - \mu)^2\)[/tex]
3. Sum of squared differences:
- Add all the squared differences calculated above:
[tex]\[
\text{Numerator} = (value1 - \mu)^2 + (value2 - \mu)^2 + (value3 - \mu)^2 + (value4 - \mu)^2 + (value5 - \mu)^2
\][/tex]
4. Division by the number of data points (N):
- The denominator is [tex]\( N \)[/tex], which is the total number of values in the data set.
Finally, the variance [tex]\(\sigma^2\)[/tex] is:
[tex]\[
\sigma^2 = \frac{\text{Numerator}}{N}
\][/tex]
### Answers:
- Numerator: [tex]\( \text{Numerator} = (value1 - \mu)^2 + (value2 - \mu)^2 + (value3 - \mu)^2 + (value4 - \mu)^2 + (value5 - \mu)^2 \)[/tex]
- Denominator: [tex]\( \text{Denominator} = N \)[/tex]
- Variance: [tex]\( \sigma^2 = \frac{\text{Numerator}}{N} \)[/tex]
Without the actual values of value1, value2, value3, value4, and value5, we cannot compute the exact numeric result, but the steps and formulas provided guide you on how it should be done.
