Numeracy Higher November 2018 Unit 2 Q1
1. Tube Cycles makes a large number of bikes each day.
(a) On 1st December 2016, 4000 bikes were made at the Tube Cycles factory.
The Tube Cycles factory was working at 80% capacity on that day.
This means that only 80% of the maximum possible number of bikes were made.
The Tube Cycles factory was working at 80% capacity on that day.
This means that only 80% of the maximum possible number of bikes were made.
When the factory works at 95% capacity, how many bikes are made in one day? [3]
(b)
(i) In October 2018, the manager of the Tube Cycles factory recorded the number of bikes made each day.
Here are her results.
Here are her results.
| Number of bikes, \(b\) | Frequency |
|---|---|
| \(1000 \leqslant b \lt 2000\) | 3 |
| \(2000 \leqslant b \lt 3000\) | 12 |
| \(3000 \leqslant b \lt 4000\) | 9 |
| \(4000 \leqslant b \lt 5000\) | 7 |
Calculate an estimate of the mean number of bikes made per day during October 2018. [4]
(ii) Which group contains the median number of bikes made per day?
Circle your answer. [1]
Circle your answer. [1]
\(1000 \leqslant b \lt 2000\) \(2000 \leqslant b \lt 3000\) \(3000 \leqslant b \lt 4000\)
\(4000 \leqslant b \lt 5000\) Can’t tell
| Scheme | Marks | Comments |
|---|---|---|
| Idea that 4000 cycles is 80% | S1 | Interpretation of link between 80% and 4000 cycles, e.g. sight of any one of the following, provided not with incorrect idea of using 20% or (95 – 80 =) 15%
|
| 95 × 4000 ÷ 80 or 95 × 50 or equivalent 4750 (cycles) | M1 A1 |
| Scheme | Marks | Comments |
|---|---|---|
| (i) Midpoints 1500, 2500, 3500, 4500 | B1 | |
| 1500×3 + 2500×12 + 3500×9 + 4500×7 (= 4500 + 30 000 + 31500 + 31500 = 97500) | M1 | FT ‘their midpoints’ provided each one lies within the appropriate group, including bounds throughout Use of lower bound gives 82 000 Use of upper bounds gives 113 000 |
| ÷ 31 | m1 | Use of lower bounds gives 2645(.16...) Use of upper bounds gives 3645(.16...) |
| 3145(.16..cycles) or 3145.2 (cycles) | A1 | |
| (ii) 3000 ≤ b < 4000 | B1 |