you create the data create a set of seven numbers (repeats allowed) that have the five numbers summary. minimum =4 Q1=8 M=12 Q3=15 Maximum=19.

Question

There is more than one set of seven numbers with this five number summary. What must be true about the seven numbers to have this five number summary

Answer 1

To start with, any 7-number set with the given 5 number summary will look like this:
4, _, _, _, _, _, 19
Since there's an odd number of pieces of data, the middle value is the median, M, so the set must also look like this:
4, _, _, 12, _, _, 19
Now think about how lower quartile and upper quartile are calculated, to see what else must be true about the 7-number set.