only the three students who had scored the highest the first time around did better. In fact, they each scored 100. The other students’ scores remained unchanged. The new set of scores is: 32, 61, 65, 67, 71, 80, 81, 81, 81, 100, 100, 100. (Carlos did not retake the test.) *Here you may copy the data in List 2 to appear in List 4 as follows: Highlight the cursor in the list name at the top of the column (L4). Press ENTER and note the cursor will be flashing at the bottom where it says “L3 = “. Type in L2 and press ENTER. The data in L2 will be listed in L4. Delete the three highest entries (83, 92, 93) and replace them with 100,100,100. What is the new mean? [76.5] The new median? [80.5] Compare these with your answers in problems 1a and 2a. Why do you suppose the mean changed when the median did not change? What does this tell you about the median? [The median is resistant to extreme scores on either the low or the high end while the mean is not. The mean is pulled in the direction of the lower or higher scores.] What if the lowest score were changed to 0? Would the mean change? [yes] Would the median? [no] (See Appendix C.)
What is the mode of Mr. Sneed’s new data set of scores? [There are two modes – 81 and 100]
C. Stem-and-Leaf Plots or Stemplots
An easy way to quickly find the median of a data set is to represent the data graphically in a stem-and-leaf plot. Use the data above in problem #1a to construct a stem-and-leaf plot for Mr. Sneed’s scores as follows:
Make a vertical line to separate the “stems” (the tens digits) from the “leaves” (the ones digits). Place the stem values to the left, and the corresponding leaf values to the right. A second run-through would enable you to put the data in numerical order by rearranging the order of the leaves.
1. Consider the shape, center and spread of the data reflected in your stem- and-leaf plot. Can you tell from the stem-and-leaf plot where the center is? Count from the lowest score to the “middle” score. Do you see how easy it is to find your median in a stem-and-leaf plot?