Solutions for Session 4, Part A

See solutions for Problems: A1 | A2 | A3 | A4

 Problem A1 You would know that the lengths of the other nine noodles must be between the lengths of these two; in other words, none of the other nine noodles can be shorter than Min, and none of them can be longer than Max.

 Problem A2 The length of noodle N4 must be between Min and Max.

 Problem A3 You would not know the mean length or the median length. You would not know whether the remaining nine noodles were closer to Min or to Max -- only that they were between those values.

 Problem A4 If you had the actual noodles or knew their lengths, you could use the mean as a "typical" value, which you find by adding the lengths of all 11 noodles and dividing the sum by 11. You could also use the median -- the noodle in the center of the ordered list (i.e., the sixth noodle). However, if you only had the information from the Two-Number Summary, your best answer would be the average of Max and Min. This number, which is sometimes called the midrange, can turn out to be very far away from the mean and median, depending on the distribution of the noodles.