Introduction

• Topic: Comparing the speed of different volleyball attacks.
• Objective: Look at the speed difference between a hard Spike and a soft Tip over the net.
• Method: Analyze a small sample dataset of 10 attacks.

The Math: Average Speed

To find the average speed of a specific attack type, we calculate the sample mean.

The formula for the sample mean is:

\[\bar{x} = \frac{\sum x_i}{n}\]

Where \(\sum x_i\) is the total sum of the speeds, and \(n\) is the number of attacks.

The Data (R Code)

library(ggplot2)
library(plotly)

volleyball_data <- data.frame(
  Attack_Type = c("Spike", "Spike", "Spike", "Spike", "Spike",
                  "Tip", "Tip", "Tip", "Tip", "Tip"),
  Speed_mph = c(45, 50, 48, 52, 47,
                15, 12, 14, 18, 16)
)

Speed Boxplot

Speed Scatter

Interactive Plot

The Math: Speed Variance

To see how much the speeds vary from hit to hit, we calculate the standard deviation.

The formula is:\[s = \sqrt{\frac{\sum(x_i - \bar{x})^2}{n-1}}\]

A higher standard deviation means the attack speeds are more unpredictable.

Conclusion

• Findings: Spikes are much faster than tips, clustering around 48 mph.

• Variability: The spread of the data (standard deviation) shows that tip speeds are slightly more consistent than spike speeds.

• Summary: The visualizations clearly demonstrate the different speed zones for the two volleyball tactics.