To calculate the range, variance, and standard deviation of a data set, we need the specific data values. Could you please provide the numbers or the data set you want to analyze?

If you already have the data set, here’s a quick overview of how each is calculated:

1. Range: The range is the difference between the maximum and minimum values in the data set. $\text{Range} = \text{Max value} - \text{Min value}$

2. Variance: Variance measures how much the data points vary from the mean (average). The formula for variance ($\sigma^2$) for a sample is: $\sigma^2 = \frac{1}{n} \sum_{i=1}^n (x_i - \mu)^2$ where:

   • $n$ is the number of data points.
   • $x_i$ is each data point.
   • $\mu$ is the mean of the data.

   For a population, divide by $n-1$ instead of $n$ to apply Bessel’s correction for better estimation.

3. Standard Deviation: The standard deviation is the square root of the variance. It gives you a sense of how spread out the data points are. $\sigma = \sqrt{\sigma^2}$

If you provide your data, I can walk through the steps and compute these values for you. Let me know!