A shop records the time taken by its customers to complete a purchase on its website - OCR - GCSE Maths - Question 3 - 2017 - Paper 1

To calculate an estimate of the mean time taken, we first need the midpoints of each time interval along with the number of customers in each interval:

• For the interval $0 < t < 3$:
  • Midpoint = $\frac{0 + 3}{2} = 1.5$,
  • Customers = 6
• For the interval $3 < t < 6$:
  • Midpoint = $\frac{3 + 6}{2} = 4.5$,
  • Customers = 10
• For the interval $6 < t < 9$:
  • Midpoint = $\frac{6 + 9}{2} = 7.5$,
  • Customers = 6
• For the interval $9 < t < 12$:
  • Midpoint = $\frac{9 + 12}{2} = 10.5$,
  • Customers = 2
• For the interval $12 < t < 15$:
  • Midpoint = $\frac{12 + 15}{2} = 13.5$,
  • Customers = 1

Now we can calculate the total time taken:

$\text{Total time} = (1.5 \times 6) + (4.5 \times 10) + (7.5 \times 6) + (10.5 \times 2) + (13.5 \times 1)$

Calculating these products gives:

• $1.5 \times 6 = 9$ minutes
• $4.5 \times 10 = 45$ minutes
• $7.5 \times 6 = 45$ minutes
• $10.5 \times 2 = 21$ minutes
• $13.5 \times 1 = 13.5$ minutes

So,

$\text{Total time} = 9 + 45 + 45 + 21 + 13.5 = 133.5$

Next, we determine the total number of customers:

$\text{Total customers} = 6 + 10 + 6 + 2 + 1 = 25$

Finally, we calculate the estimated mean time taken:

$\text{Mean time} = \frac{\text{Total time}}{\text{Total customers}} = \frac{133.5}{25} = 5.34 \text{ minutes}$