The suitable average for averaging the shoe sizes of children is the mode. The mode is the value that appears most frequently in a dataset, and in this case, it would be the shoe size that is most common among the children. The mode is a suitable average for this scenario because it is the most representative value of the dataset, and it is not affected by extreme values or outliers. The mean, harmonic mean, and geometric mean are not suitable averages for this scenario because they are affected by extreme values or outliers, and they may not be representative of the dataset. The percentile is not an average but a measure of the position of a value in a dataset relative to other values.