Numeracy Intermediate November 2017 Unit 1 Q12
12. Lena has three apple trees in her garden.
She has one Gala apple tree, one Orange Pippin tree and one Pink Lady tree.
She picks 50 apples from each of the 3 trees.
She records the width of each apple, as shown.
Lena constructs box and whisker diagrams for the widths of the apples collected from each of the three trees.
(a) Complete each of the following statements.
(i) ‘Apples from the …………… apple tree have the least median width.
The median width of apples recorded for this tree is …………… mm.’ [1]
The median width of apples recorded for this tree is …………… mm.’ [1]
(ii) ‘The range of the widths of apples recorded for the Gala apple tree
is …………… mm.’ [1]
is …………… mm.’ [1]
(iii) ‘The …………… apple tree has apples with the greatest interquartile range of widths.
The interquartile range of the widths of apples recorded for this tree
is …………… mm.’ [2]
The interquartile range of the widths of apples recorded for this tree
is …………… mm.’ [2]
(b) Which tree has a higher proportion of larger apples?
You must give a reason for your answer. [1]
You must give a reason for your answer. [1]
| Scheme | Marks | Comments |
|---|---|---|
| (i) Orange pippin and 57 (mm) | B1 | Accept ‘orange’ or ‘pippin’ as indication of the correct tree |
| (ii) 41 (mm) | B1 | |
| (iii) Pink Lady and 33 (mm) | B2 | B1 for any of the following:
|
| Scheme | Marks | Comments |
|---|---|---|
| Gala selected with a reason e.g. '(highest) upper quartile', ‘25% over 80 mm’ OR Pink Lady selected with a reason e.g. ‘(highest) median’, ‘half are over 63 mm’ | B1 | Ignore units throughout Do not accept reasons based on range or IQR Do not ignore any additional statements of range, IQR, lower quartile Ignore an incorrect median stated for Pink Lady, e.g. 66mm, provided it is >61 and <67(mm) |
Corrected by Westie's Workshop
- The board's mark scheme printed “Do not ignore additional any statements”. Changed to “Do not ignore any additional statements” because the words “additional” and “any” are in the wrong order.
Original: see the board's mark scheme PDF (link above).