(a) A stem-and-leaf diagram includes all raw data, allowing for further statistical processes such as finding the frequency, mean, mode, or standard deviation, which cannot be found using a box-and-whisker plot.

(b) The back-to-back stem-and-leaf diagram is drawn with Amazons on the left and Giants on the right. The stems are the tens digits, and the leaves are the units digits of the heights. See the mark-scheme for the correct diagram.

(c) To find the interquartile range (IQR) of the Amazons' heights, first order the data: 178, 181, 182, 184, 190, 196, 198, 201, 202, 205, 215. The lower quartile (LQ) is the median of the first half: 182 cm. The upper quartile (UQ) is the median of the second half: 202 cm. Therefore, the IQR is calculated as:

\(\text{IQR} = UQ - LQ = 202 - 182 = 20 \text{ cm}\)

(d) Let the height of the fourth new player be \(h\). The sum of the original 11 players' heights is 2132 cm. The sum of the heights of all 15 players is:

\(191.2 \times 15 = 2868 \text{ cm}\)

The sum of the heights of the four new players is:

\(180 + 185 + 190 + h = 555 + h\)

Equating the total heights:

\(2132 + 555 + h = 2868\)

\(2687 + h = 2868\)

\(h = 2868 - 2687 = 181 \text{ cm}\)

(a) Back-to-back stem-and-leaf diagram (stem = tens, leaf = units; Dados on the left, Linva on the right):

Key: \( 6 \mid 3 \mid 2 \) means \(36\) cm (Dados) and \(32\) cm (Linva).

(b) Dados ordered: 6, 8, 10, 10, 12, 15, 16, 22, 28, 36, 42.

Median \(= 15\ \text{cm}\).

Lower quartile \(Q_1 = 10\ \text{cm}\), upper quartile \(Q_3 = 28\ \text{cm}\).

Interquartile range: \( \text{IQR} = Q_3 - Q_1 = 28 - 10 = 18\ \text{cm}. \)

(c) Linva: median \(=12\ \text{cm}\), \(Q_1=9\ \text{cm}\), \(Q_3=32\ \text{cm}\) so \( \text{IQR}=23\ \text{cm} \).

Dados has higher central tendency (median \(15\ \text{cm}\) vs \(12\ \text{cm}\)) but smaller spread (IQR \(18\ \text{cm}\) vs \(23\ \text{cm}\)).

On average the snowfall in Davos is higher.

The amount of snowfall in Linva varies more than in Davos.

(a)

Key: \( 1 \mid 4 \mid 2 \) means \(\$41{,}000 \)(Company A) and \(\$42{,}000\) (Company B).

(b) Ordered salaries (A): 30, 32, 35, 41, 41, 42, 47, 49, 52, 53, 64.

Median \(=\) 6th value \(= \$42{,}000\).

Lower quartile \(Q_1 = \$35{,}000\); upper quartile \(Q_3 = \$52{,}000\).

Interquartile range \( \text{IQR} = Q_3 - Q_1 = \$52{,}000 - \$35{,}000 = \$17{,}000 \).

(c) Sum of given 11 salaries (B): \(\$433{,}000\).

Total for 12 employees: \(38{,}500 \times 12 = \$462{,}000\).

New employee’s salary: \( \$462{,}000 - \$433{,}000 = \$29{,}000 \).

(i)

Key: \( 8 \mid 4 \mid 5 \) represents \(48\) minutes (Thaters School) and \(45\) minutes (Whitefay Park School).

(ii) Ordered times (Thaters): 38, 43, 48, 52, 54, 56, 57, 58, 58, 61, 62, 66, 75.

Lower quartile \(Q_1 = \frac{48 + 52}{2} = 50\).

Upper quartile \(Q_3 = \frac{61 + 62}{2} = 61.5\).

Interquartile range \( \text{IQR} = Q_3 - Q_1 = 61.5 - 50 = 11.5 \) minutes.

(i)

Key: \( 3 \mid 6 \mid 4 \) means 63 kg for Dolphins and 64 kg for Sharks.

(ii) Ordered weights (Dolphins): 62, 63, 65, 65, 69, 72, 73, 75, 80, 82, 82.

Median = 72 kg (middle value).

Lower quartile \(Q_1 = 65\) kg, upper quartile \(Q_3 = 80\) kg.

Interquartile range \( \text{IQR} = Q_3 - Q_1 = 80 - 65 = 15 \) kg.