Questions: The data to the right represent the top speed (in kilometers per hour) of all the players (except goaltenders) in a certain soccer league. Construct (a) a relative frequency distribution (b) a frequency histogram, and (c) a relative frequency histogram. What percentage of players had a top speed between 26 and 29.9 km/h? What percentage of players had a top speed less than 13.9 km/h? Speed (km/hr) Number of Players 10-13.9 3 14-17.9 8 18-21.9 18 22-25.9 72 26-29.9 305 30-33.9 235

The data to the right represent the top speed (in kilometers per hour) of all the players (except goaltenders) in a certain soccer league. Construct (a) a relative frequency distribution (b) a frequency histogram, and (c) a relative frequency histogram. What percentage of players had a top speed between 26 and 29.9 km/h? What percentage of players had a top speed less than 13.9 km/h? Speed (km/hr) Number of Players 10-13.9 3 14-17.9 8 18-21.9 18 22-25.9 72 26-29.9 305 30-33.9 235
Transcript text: The data to the right represent the top speed (in kilometers per hour) of all the players (except goaltenders) in a certain soccer league. Construct (a) a relative frequency distribution (b) a frequency histogram, and (c) a relative frequency histogram. What percentage of players had a lop speed between 26 and $29.9 \mathrm{~km} / \mathrm{h}$ ? What percentage of players had a top speed less than $13.9 \mathrm{~km} / \mathrm{h}$ ? \begin{tabular}{cc} \hline Speed (km/hr) & Number of Players \\ \hline $10-13.9$ & 3 \\ $14-17.9$ & 8 \\ $18-21.9$ & 18 \\ $22-25.9$ & 72 \\ $26-29.9$ & 305 \\ $30-33.9$ & 235 \\ & \end{tabular}
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Solution

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Solution Steps

Step 1: Construct a Relative Frequency Distribution

To construct a relative frequency distribution, we divide the number of players in each speed range by the total number of players. For speed range 10-13.9 km/hr, the relative frequency is calculated as 3 / 641 = 0 For speed range 14-17.9 km/hr, the relative frequency is calculated as 8 / 641 = 0.01 For speed range 18-21.9 km/hr, the relative frequency is calculated as 18 / 641 = 0.03 For speed range 22-25.9 km/hr, the relative frequency is calculated as 72 / 641 = 0.11 For speed range 26-29.9 km/hr, the relative frequency is calculated as 305 / 641 = 0.48 For speed range 30-33.9 km/hr, the relative frequency is calculated as 235 / 641 = 0.37

Step 2: Construct a Frequency Histogram

A frequency histogram is constructed with speed ranges on the x-axis and the number of players on the y-axis. Each bar represents a speed range, and the height of the bar corresponds to the number of players in that range. Speed Range: 10-13.9 km/hr, Number of Players: 3 Speed Range: 14-17.9 km/hr, Number of Players: 8 Speed Range: 18-21.9 km/hr, Number of Players: 18 Speed Range: 22-25.9 km/hr, Number of Players: 72 Speed Range: 26-29.9 km/hr, Number of Players: 305 Speed Range: 30-33.9 km/hr, Number of Players: 235

Step 3: Construct a Relative Frequency Histogram

A relative frequency histogram is similar to the frequency histogram, but the height of each bar corresponds to the relative frequency of players in each speed range. Speed Range: 10-13.9 km/hr, Relative Frequency: 0 Speed Range: 14-17.9 km/hr, Relative Frequency: 0.01 Speed Range: 18-21.9 km/hr, Relative Frequency: 0.03 Speed Range: 22-25.9 km/hr, Relative Frequency: 0.11 Speed Range: 26-29.9 km/hr, Relative Frequency: 0.48 Speed Range: 30-33.9 km/hr, Relative Frequency: 0.37

Step 4: Calculate Specific Percentages

To find the percentage of players within a specific speed range, multiply the relative frequency by 1. Percentage of players in speed range 10-13.9 km/hr: 0% Percentage of players in speed range 14-17.9 km/hr: 1% Percentage of players in speed range 18-21.9 km/hr: 3% Percentage of players in speed range 22-25.9 km/hr: 11% Percentage of players in speed range 26-29.9 km/hr: 48% Percentage of players in speed range 30-33.9 km/hr: 37%

Final Answer:

The analysis includes a relative frequency distribution, a frequency histogram, a relative frequency histogram, and the calculation of specific percentages within the speed ranges.

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