Question

the following frequency table shows the number of goals scored by members of a soccer team in a given season. fill in the blanks to complete the corresponding relative frequency table. \

$$\begin{tabular}{|l|l|} \\hline data & frequency \\\\ \\hline 1 & 8 \\\\ \\hline 2 & 3 \\\\ \\hline 3 & 12 \\\\ \\hline 8 & 11 \\\\ \\hline 10 & 7 \\\\ \\hline \\end{tabular}$$

provide your answer below: \

$$\begin{tabular}{|c|c|c|} \\hline data (goals scored) & frequency & relative frequency \\\\ \\hline 1 & 8 & $\\frac{8}{50}$ \\\\ \\hline 2 & 3 & $\\square$ \\\\ \\hline 3 & 12 & $\\frac{12}{50}$ \\\\ \\hline 4 & 9 & $\\square$ \\\\ \\hline 8 & 11 & $\\frac{11}{50}$ \\\\ \\hline 10 & 7 & $\\square$ \\\\ \\hline \\end{tabular}$$

Explanation:

Step1: Find total frequency

First, we calculate the total number of observations (total frequency). We sum up all the frequencies: \(8 + 3+12 + 9+11 + 7=50\). This is consistent with the first relative frequency denominator (\(50\)).

Step2: Calculate relative frequency for data value 2

Relative frequency is calculated as \(\frac{\text{Frequency}}{\text{Total Frequency}}\). For data value 2, frequency is 3, so relative frequency is \(\frac{3}{50}\).

Step3: Calculate relative frequency for data value 4

For data value 4, frequency is 9, so relative frequency is \(\frac{9}{50}\).

Step4: Calculate relative frequency for data value 10

For data value 10, frequency is 7, so relative frequency is \(\frac{7}{50}\).

Answer:

For data value 2: \(\frac{3}{50}\)
For data value 4: \(\frac{9}{50}\)
For data value 10: \(\frac{7}{50}\)

So the completed relative frequency table (for the blanks) has:

• For 2: \(\frac{3}{50}\)
• For 4: \(\frac{9}{50}\)
• For 10: \(\frac{7}{50}\)