To solve the frequency part:

Step 1: Verify Data

From the table:

1. # of Vehicles (x): 0, 1, 2, 3, 4, 5
2. Frequency (f): 3, 6, 7, 9, 6, 4

Step 2: Compute Relative Frequency

Relative frequency = $\frac{\text{frequency}}{\text{total frequency}}$

• Total frequency = $3 + 6 + 7 + 9 + 6 + 4 = 35$
• Calculations:
  • $0: \frac{3}{35} = 0.0857$
  • $1: \frac{6}{35} = 0.1714$
  • $2: \frac{7}{35} = 0.2000$
  • $3: \frac{9}{35} = 0.2571$
  • $4: \frac{6}{35} = 0.1714$
  • $5: \frac{4}{35} = 0.1143$

Step 3: Compute Weighted Terms

Weighted term = $x \cdot \text{relative frequency}$

• Calculations:
  • $0: 0 \cdot 0.0857 = 0.0000$
  • $1: 1 \cdot 0.1714 = 0.1714$
  • $2: 2 \cdot 0.2000 = 0.4000$
  • $3: 3 \cdot 0.2571 = 0.7714$
  • $4: 4 \cdot 0.1714 = 0.6857$
  • $5: 5 \cdot 0.1143 = 0.5714$

Step 4: Compute the Mean

Mean = $\sum (\text{weighted terms})$

• $\text{Sum of weighted terms} = 0.0000 + 0.1714 + 0.4000 + 0.7714 + 0.6857 + 0.5714 = 2.6000$

Final Answer:

• Mean: $2.6$

Would you like further details or clarifications?

Here are 5 related questions to explore:

1. How is the median determined in a frequency table?
2. What is the role of cumulative frequency in identifying percentiles?
3. How would the mean change if another vehicle count was added?
4. Can you use Excel formulas to automate this process?
5. Why is relative frequency important in probability studies?

Tip: Always ensure the sum of relative frequencies equals 1 for verification.