Calculate the estimated mean speed of 200 cars using the provided grouped frequency data.

For grouped frequency data, the mean is estimated by using the midpoint of each class interval.

• For $0 < v \le 20$, midpoint $x_1 = \frac{0+20}{2} = 10$
• For $20 < v \le 40$, midpoint $x_2 = \frac{20+40}{2} = 30$
• For $40 < v \le 45$, midpoint $x_3 = \frac{40+45}{2} = 42.5$
• For $45 < v \le 50$, midpoint $x_4 = \frac{45+50}{2} = 47.5$
• For $50 < v \le 60$, midpoint $x_5 = \frac{50+60}{2} = 55$
• For $60 < v \le 80$, midpoint $x_6 = \frac{60+80}{2} = 70$

• $10 \times 16 = 160$
• $30 \times 34 = 1020$
• $42.5 \times 62 = 2635$
• $47.5 \times 58 = 2755$
• $55 \times 26 = 1430$
• $70 \times 4 = 280$

Sum of products $\sum fx = 160 + 1020 + 2635 + 2755 + 1430 + 280 = 8280$
Sum of frequencies $\sum f = 16 + 34 + 62 + 58 + 26 + 4 = 200$ (This matches the total of 200 cars given in the question).

The formula for the estimated mean is $\bar{x} = \frac{\sum fx}{\sum f}$.

The estimate of the mean speed is $41.4 \text{ km/h}$.