Question

the ages and masses of vehicles of drivers who received speeding tickets in the past 30 days is shown in the table below. use this information to answer parts a through c.

age groups	under 1500 kg	over 1500 kg
26 - 35	190	173
36 - 45	154	160
46 - 55	80	82
>= 56	124	161

(c) construct a side-by-side relative frequency bar graph. choose the correct graph below where in each age grouping, the left bar represents vehicles under 1500 kg and the right bar represents vehicles over 1500 kg

○ a. bar graph with specific heights
○ b. bar graph with specific heights
○ c. bar graph with specific heights

Explanation:

To solve part (c), we first calculate the total number of drivers:

Step 1: Calculate Total Frequency

For each age group, sum the number of vehicles under and over 1500 kg:

• \( 16 - 25 \): \( 269 + 224 = 493 \)
• \( 26 - 35 \): \( 190 + 173 = 363 \)
• \( 36 - 45 \): \( 154 + 160 = 314 \)
• \( 46 - 55 \): \( 80 + 82 = 162 \)
• \( \geq 56 \): \( 124 + 161 = 285 \)

Total \( = 493 + 363 + 314 + 162 + 285 = 1617 \)

Step 2: Calculate Relative Frequencies

For each age group and vehicle mass category, divide by the total:

• 16 - 25:
• Under 1500 kg: \( \frac{269}{1617} \approx 0.166 \)
• Over 1500 kg: \( \frac{224}{1617} \approx 0.139 \)
• 26 - 35:
• Under 1500 kg: \( \frac{190}{1617} \approx 0.117 \)
• Over 1500 kg: \( \frac{173}{1617} \approx 0.107 \)
• 36 - 45:
• Under 1500 kg: \( \frac{154}{1617} \approx 0.095 \)
• Over 1500 kg: \( \frac{160}{1617} \approx 0.099 \)
• 46 - 55:
• Under 1500 kg: \( \frac{80}{1617} \approx 0.049 \)
• Over 1500 kg: \( \frac{82}{1617} \approx 0.051 \)
• ≥ 56:
• Under 1500 kg: \( \frac{124}{1617} \approx 0.077 \)
• Over 1500 kg: \( \frac{161}{1617} \approx 0.099 \)

Step 3: Analyze the Graphs

• Graph A: Left bars (under 1500 kg) for 16 - 25, 26 - 35, 36 - 45 are taller than right bars (over 1500 kg). For ≥ 56, left bar is shorter. For 46 - 55, both are short. This matches our relative frequencies.
• Graph B: For ≥ 56, right bar is taller, but our calculation shows over 1500 kg (≈0.099) and under (≈0.077) – right is taller, but 46 - 55: over (≈0.051) is taller than under (≈0.049), but in B, 46 - 55 left and right are similar? No, our 46 - 55 under ≈0.049, over ≈0.051 (close). But 36 - 45: under ≈0.095, over ≈0.099 (close). In B, 36 - 45 left and right are same? No, our 36 - 45 under is slightly less than over. But 16 - 25: under ≈0.166, over ≈0.139 (left taller). 26 - 35: under ≈0.117, over ≈0.107 (left taller). So B’s 36 - 45 and ≥56 may not match.
• Graph C: For 26 - 35, right bar (over 1500 kg) is taller, but our 26 - 35 over ≈0.107, under ≈0.117 (left should be taller). So C is incorrect.

Answer:

A