20N.1.SL.TZ0.T_7

pestleMathematicsAISLPaper 120N· sl-4-3-mean-median-mode-mean-of-grouped-data-standard-deviation-quartiles-iqrsource ↗

Anne-Marie planted four sunflowers in order of height, from shortest to tallest.

Flower $C$ is $32 cm$ tall.

The median height of the flowers is $24 cm$ .

The range of the heights is $50 cm$ . The height of Flower $A$ is $p cm$ and the height of Flower $D$ is $q cm$ .

The mean height of the flowers is $27 cm$ .

Find the height of Flower $B$ .

[2]

Using this information, write down an equation in $p$ and $q$ .

[1]

Write down a second equation in $p$ and $q$ .

[1]

Using your answers to parts (b) and (c), find the height of Flower $A$ .

[1]

d.i.

Using your answers to parts (b) and (c), find the height of Flower $D$ .

[1]

d.ii.

Markscheme / solution

* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.

$24 - 8$ OR $24 - (32 - 24)$ OR $24 = \frac{32 + h}{2}$ (M1)

Note: Award (M1) for subtracting $8$ from the median, or equivalent.

$16 (cm)$ (A1) (C2)

[2 marks]

$q - p = 50$ (or equivalent) (A1) (C1)

[1 mark]

$\frac{p + 16 + 32 + q}{4} = 27$ OR $p + q = 60$ (or equvalent) (A1)(ft) (C1)

Note: Follow through from part (a).

[1 mark]

$5 (cm)$ (A1)(ft) (C1)

Note: Follow through from parts (b) and (c).

[1 mark]

d.i.

$55 (cm)$ (A1)(ft) (C1)

Note: Follow through from parts (b) and (c).

[1 mark]

d.ii.

Examiners’ report

[N/A]

d.i.

[N/A]

d.ii.