Solution

(i) The back-to-back stem-and-leaf diagram is constructed as follows:

Key: \( 9 \mid 4 \mid 2 \) represents \(0.049\ \text{g}\) (Factory A) and \(0.042\ \text{g}\) (Factory B).

(ii) To find the median and interquartile range for factory B:

Ordered masses: \( 0.031,\ 0.035,\ 0.038,\ 0.042,\ 0.044,\ 0.047,\ 0.048,\ 0.049,\ 0.051,\ 0.054,\ 0.056,\ 0.058,\ 0.064 \).

Median \(= 0.048\ \text{g}\).

Lower quartile \(Q_1 = 0.040\ \text{g}\), upper quartile \(Q_3 = 0.055\ \text{g}\).

\( \text{IQR} = Q_3 - Q_1 = 0.055 - 0.040 = 0.015\ \text{g} \).

(iii) Comparisons:

• The masses are generally heavier in factory A.
• The masses are more spread out in factory B.