The masses, mg, of some parcels are shown below - OCR - GCSE Maths - Question 16 - 2020 - Paper 1

To verify that 70 students completed the race within 45 to 50 minutes, we need to analyze the histogram. The ranges for the bins must be calculated based on the frequency densities shown. By calculating the area under the histogram for the interval 45-50 minutes, we can derive the total number of students that fall within this time frame:

• For the interval 45-50 minutes, the height of the bar is determined by the frequency density value, which must be multiplied by the width of the interval to yield the total frequency.

If the heights of the bars and their corresponding intervals indicate a value summing up to 70, it confirms that the number of students within that range is indeed 70.

To find the mean time taken to complete the race, we will calculate the midpoints of each interval (time) multiplied by their corresponding frequencies:

1. Identify the midpoints for all time intervals based on the histogram.
2. Multiply each midpoint by the frequency (height of the histogram) for that interval, summing these products.
3. Divide the total of these products by the total number of students (which is 70).

Mathematically, the mean can be represented as:

$ext{Mean} = \frac{\sum (midpoint \times frequency)}{total\ students}$

This will yield an estimate for the mean time taken.