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The police record the speed of vehicles passing a speed checkpoint - OCR - GCSE Maths - Question 2 - 2018 - Paper 6
Question 2
The police record the speed of vehicles passing a speed checkpoint. The speeds are recorded in the table below. Speed (s mph) Number of vehicles 0 < s ≤ 20 ... show full transcript
Worked Solution & Example Answer:The police record the speed of vehicles passing a speed checkpoint - OCR - GCSE Maths - Question 2 - 2018 - Paper 6
Step 1
Calculate an estimate of the mean speed of the vehicles.
Answer
To estimate the mean speed, we use the midpoints of each speed range and multiply them by the number of vehicles in each range. The midpoints are as follows:
- For the range 0 < s ≤ 20: midpoint = 10, vehicles = 5
- For the range 20 < s ≤ 40: midpoint = 30, vehicles = 8
- For the range 40 < s ≤ 50: midpoint = 45, vehicles = 37
- For the range 50 < s ≤ 60: midpoint = 55, vehicles = 47
- For the range 60 < s ≤ 80: midpoint = 70, vehicles = 3
The estimated mean speed is calculated as follows:
-
Calculate the total speed contribution:
- (10 * 5) + (30 * 8) + (45 * 37) + (55 * 47) + (70 * 3)
- = 50 + 240 + 1665 + 2585 + 210
- = 1950 + 1665 + 2585 + 210 = 5700
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Calculate the total number of vehicles:
- 5 + 8 + 37 + 47 + 3 = 100
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Finally, calculate the estimated mean speed: mph.
Step 2
Explain why it is not possible to use the information from this table to calculate the exact value of the mean speed.
Answer
The exact speeds for each vehicle are not recorded in the table. Only the ranges and the number of vehicles within those ranges are provided. Therefore, we cannot determine the exact mean speed, as we do not know the specific speeds of the vehicles within each range.