Teacher resources and professional development across the curriculum

Teacher professional development and classroom resources across the curriculum

Solutions for Session 4, Part B

See solutions for Problems: B1 | B2 | B3 | B4 | B5 | B6| B7

 Problem B1 You would know that there must be exactly five noodles shorter than the median noodle and five noodles longer than the median noodle.

 Problem B2 You would not know the actual values of any of the other noodles: The five shorter noodles could be extremely short, the five longer noodles could be many feet long, they could all be fairly close in size to the median, etc. You would also not know or be able to estimate the maximum or minimum length of the other noodles.

 Problem B3 You would know that all of the noodles are between Min and Max, and you can divide the noodles into two equal groups: five that are shorter than Med (including Min) and five that are longer than Med (including Max). This information gives you two specific intervals that contain an equal number of noodles, and all of the noodles are contained in these intervals. This is different from Problem A3, where you knew nothing about the size of the noodles between Min and Max, and from Problem B1, where you knew nothing about the upper and lower boundaries of your data set.

 Problem B4 You still wouldn't know the lengths of the noodles in the two intervals between Min and Med, or between Med and Max. These noodles could be very close to Med, very close to the extreme values, evenly spread within the intervals, or something else entirely. There is no way to know without more information.

 Problem B5 You would know that N4 must be larger than Min, smaller than Med, and smaller than Max. This is true because N6 is the median, and N4 must be smaller than N6. You still wouldn't know N4's actual value or whether N4 was closer to Min or to Med. (A common mistake is to claim that N4 must be closer to Med than it is to Min. This is not necessarily true, since the values of N2 through N5 can be anywhere in the interval between Min and Med; for example, they could all be very close to Min.)

 Problem B6 There are two noodles left, the sixth and the seventh. Neither of these two noodles can serve as the median, so we need to do something else.

 Problem B7 You would know that there are six noodles that are shorter than the median, and six that are longer.

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