Numeracy Higher November 2019 Unit 2 Q3
3.
(a) 40 people were asked how many mugs they have in their cupboards.
The results are shown below.
The results are shown below.
| Number of mugs | Frequency |
|---|---|
| 1 to 5 | 3 |
| 6 to 10 | 7 |
| 11 to 15 | 12 |
| 16 to 20 | 18 |
(i) From this data, which group contains the median number of mugs?
Circle your answer. [1]
Circle your answer. [1]
Can’t tell 1 to 5 6 to 10 11 to 15 16 to 20
(ii) Calculate an estimate of the mean number of mugs these people have in their cupboards. [4]
(b) A cylindrical mug has an inner radius of 4·3 cm and an inner height of 11·8 cm.
Tea is poured into the mug.
The level of the tea is 2 cm below the top of the mug.
Calculate the volume of the tea in the mug. [3]
| Scheme | Marks | Comments |
|---|---|---|
| (i) 11 to 15 | B1 | |
| (ii) Midpoints 3, 8, 13, 18 | B1 | |
| 3×3 + 8×7 + 13×12 + 18×18 (9 + 56 + 156 + 324 = 545) | M1 | FT ‘their midpoints’ provided at least 3 of ‘their 4 midpoints’ lie within the appropriate group, including lower and upper bounds Use of lower bound gives 465 Use of upper bounds gives 625 |
| ÷ 40 | m1 | |
| 13.6(25 mugs) | A1 | Allow 13 or 14 (mugs) from correct working Use of lower bounds gives 11.625 (allow 11 or 12) use of upper bounds gives 15.625 (allow 15 or 16) |
| Scheme | Marks | Comments |
|---|---|---|
| (Volume) π × 4.32 × (11.8 – 2) or equivalent | M2 | Accept methods shown in stages Allow M1 for sight of π × 4.32 × 11.8 or π × 4.32 × 2, including if embedded or included with incorrect working. |
| Answer in the range 568 (cm3) to 569.4 (cm3) | A1 | CAO. Accept \(\dfrac{90601\pi}{500}\) or 181.2(02..)π Provided M1 previously awarded then also award SC1 for an answer in the range
|