The formula to calculate the Average Squared Distance (ASD) is:
\[ \text{ASD} = \frac{\text{SSD}}{\text{N}} \]
Where:
Let's say the sum of squared distances (SSD) is 200 and the number of points (N) is 10. Using the formula:
\[ \text{ASD} = \frac{200}{10} = 20 \, \text{units}^2 \]
So, the average squared distance is 20 units².
Definition: This calculator estimates the distance across a square (diagonal) based on its side length.
Formula: \( d = a \sqrt{2} \)
Example: \( d = 5 \sqrt{2} \)
Definition: Calculating average distance involves finding the mean distance between multiple points.
Formula: \( \text{Average Distance} = \frac{\sum \text{Distances}}{n} \)
Example: \( \text{Average Distance} = \frac{(10 + 15 + 20)}{3} \)
Definition: Calculating miles squared involves determining the area in square miles.
Formula: \( \text{Square Miles} = \text{Length} \times \text{Width} \)
Example: \( \text{Square Miles} = 5 \times 4 \)
Definition: Mean squared distance is the average of the squares of the distances from the mean.
Formula: \( \text{Mean Squared Distance} = \frac{\sum (x_i - \bar{x})^2}{n} \)
Example: \( \text{Mean Squared Distance} = \frac{(3-4)^2 + (5-4)^2 + (4-4)^2}{3} \)
Definition: This is the average of the squared distances of each data point from the sample mean.
Formula: \( \text{Average Squared Distance} = \frac{\sum (x_i - \bar{x})^2}{n} \)
Example: \( \text{Average Squared Distance} = \frac{(2-3)^2 + (4-3)^2 + (3-3)^2}{3} \)
Definition: The formula to calculate the average distance between multiple points.
Formula: \( \text{Average Distance} = \frac{\sum \text{Distances}}{n} \)
Example: \( \text{Average Distance} = \frac{(8 + 12 + 16)}{3} \)
