To find the variance given the arithmetic mean, let’s break down the process step by step.

Understanding Arithmetic Mean
- The arithmetic mean (average) is calculated as the sum of all data points divided by the number of data points.
- In this case, the arithmetic mean is given as 8 4/2, which simplifies to 8 + 2 = 10.

Understanding Variance
- Variance measures the spread of a set of numbers. It is the average of the squared differences from the mean.
- The formula for variance (σ²) is:
σ² = Σ (xi - μ)² / N
where:
- σ² = variance
- Σ = sum of
- xi = each data point
- μ = mean
- N = number of data points

Steps to Calculate Variance
1. **Collect Data Points**: Gather the dataset for which you want to find the variance.
2. **Calculate the Mean**: Here, the mean (μ) is already calculated as 10.
3. **Find Squared Differences**: For each data point (xi), calculate (xi - μ)².
4. **Sum of Squared Differences**: Add all the squared differences together.
5. **Divide by N**: Finally, divide the sum of squared differences by the number of data points (N) to find the variance.

Example Calculation
- Suppose you have data points: 6, 8, 10, 12, 14.
- Mean (μ) = 10.
- Squared differences:
- (6 - 10)² = 16
- (8 - 10)² = 4
- (10 - 10)² = 0
- (12 - 10)² = 4
- (14 - 10)² = 16
- Sum = 16 + 4 + 0 + 4 + 16 = 40.
- Number of data points (N) = 5.
- Variance (σ²) = 40 / 5 = 8.
Thus, the variance of this dataset is 8.