Which of the following is a synonym for 'extrapolate'?

The term 'extrapolate' refers to the process of extending observations or findings beyond the original data set to make predictions or derive conclusions about unknown or unobserved situations. It involves inferring or estimating values based on existing evidence, often used in statistical and scientific contexts.

'Conjecture' aligns closely with this idea as it means to form an opinion or hypothesis based on incomplete information. When one extrapolates, they make a conjecture about potential outcomes or trends based on the data they have. This process entails not just guessing, but engaging in a reasoned evaluation to project outcomes beyond what is directly observable.

In contrast, the other options—demonstrate, analyze, and clarify—focus more on explaining, breaking down information, or making something clear, rather than inferring conclusions based on available data. They do not capture the essence of making predictions or extending knowledge as 'extrapolate' and 'conjecture' do. Thus, 'conjecture' is the most fitting synonym for 'extrapolate.'