Final answer:
To complete the frequency tree, calculate the number of men, establish how many men like cake, deduce the number of women who like cake, and then fill in the frequency tree with these figures.
Step-by-step explanation:
The question involves completing a frequency tree based on the given data, which is a part of the statistics branch of mathematics. There are 92 people, with 50 being women and 49 overall liking cake. If 20 men do not like cake, we first calculate the number of men which is 92 people minus 50 women, resulting in 42 men. Next, we subtract the 20 men who do not like cake from the total number of men to find that 22 men do like cake. Adding the 22 men who like cake to the 49 people who like cake, we can deduce that there must be 27 women who like cake since 49 - 22 = 27. Using these figures, we can fill in the frequency tree accordingly.