Course Guide - USAID Teacher Education Project

horizontal line on centimetre grid paper, one number in each cell. Have them cut outthe strip of paper and fold it in half. What do they notice? (That the crease falls onthe middle number, in this case, 5.)The point of using these two hands-on methods is to give students a direct experiencein understanding the median. However, with larger data sets counting from each endcould cause errors and a strip of paper 43 cells long would be unwieldy.Now that they have an understanding of the median as the middle number of a dataset, it is appropriate to introduce the formula where "n" is the number of entries: (n +1)/2. In the case of the above data set with 7 entries, this would be (7 + 1)/2 or 8/2.This gives the number 4, indicating that the median is the fourth number in the dataset, which in this case is 5.Note that all of three of the above examples referred to an odd-numbered data set.Ask students what would happen if you added another entry to the set, perhaps theoutlier, 20. The new data set would be 2, 2, 3, 5, 7, 8, 9, 20. What is the mediannow?Have them explore this question by using the above three methods: 1) counting fromthe end, 2) folding the numbered paper strip, and 3) using the formula. What do theynotice?Given that the median is between two numbers, ask what they think they should donow? (This is relatively easy to do, since the number 6 is right between the 5 and the7.) Ask if they think that the median of a data set can be a number not in the data set.Challenge them to find the median in this short data set: 8, 12, 20, 38. In this case themedian is still halfway between the 12 and the 20, but it is not part of a naturalsequence as was 5, 6, 7.Have students find the median of 2 and 5 as in the case of the median number ofchildren per family in two families, one of which has 2 children and the other has 5children. In this case the median in this even-numbered data set will be 3.5. Askstudents to interpret this answer as it applies 1) to a real life situation and 2) tomathematics without a context.e) End the session by noting that when students found the median for a data set withan even number of entries they were using a strategy that will be discussed more fullyin the next session: the arithmetic mean.5. Assignments (to be determined by instructor)