Neeraj from Wilson's School noticed that sets A, D and E had more values greater than 70 than sets B, C and E.
 
 
Elliot from Wilson's School used the range:
 
I used the ranges of each set of data, to work out which sets go together. Alison's temperatures were more likely to have a greater range, whereas Charlie's data, on the weights of teenagers, is likely to have a small range. Therefore, I concluded that A, D and E, which have the largest ranges, were the temperatures, while B, C and F were the teenager's weights. 
 
Randolph and Ethan, both from the USA, and Jelle from the Netherlands used another measure of spread, the standard deviation of each set:

The standard deviations for each set (to 3 decimal places) are:
A: 10.826
B: 4.527
C: 5.756
D: 9.520
E: 10.742
F: 5.229

ADE belongs to Alison
BCF belongs to Charlie 
 
Finally, here is Niharika's solution which uses several different approaches.