The police record the speed of vehicles passing a speed checkpoint - OCR - GCSE Maths - Question 17 - 2018 - Paper 1

To estimate the mean speed of the vehicles, we use the midpoint of each speed range:

1. The midpoints are:

   • For $0 < s < 20$: midpoint = 10 mph
   • For $20 < s < 40$: midpoint = 30 mph
   • For $40 < s < 50$: midpoint = 45 mph
   • For $50 < s < 60$: midpoint = 55 mph
   • For $60 < s < 80$: midpoint = 70 mph

2. Now, we multiply each midpoint by the number of vehicles in each category:

   • $10 imes 5 = 50$
   • $30 imes 8 = 240$
   • $45 imes 37 = 1665$
   • $55 imes 47 = 2585$
   • $70 imes 3 = 210$

3. Next, we sum these products:

   $50 + 240 + 1665 + 2585 + 210 = 4740$

4. The total number of vehicles is:

   $5 + 8 + 37 + 47 + 3 = 100$

5. Finally, we calculate the estimated mean speed:

   $ext{Mean speed} = \frac{4740}{100} = 47.4\text{ mph}$

Therefore, the estimated mean speed of the vehicles is approximately 47.5 mph.