Sample Midterm I

  1. The median is C. The mean is B. The mode is D. The mean is drawn toward the longer tail.
  2. No, there was no control group. This was not an experimental study at all. It turns out that lithium carbonate is poisonous and the truth is he poisoned the poor guinea pigs who were listless in their nauseous overdose. But, that's serendipity for you. Lithium, it turns out, is effective at treating mania. And it's effectiveness was discovered completely by accident when this Australian psychiatrist came up with an incorrect theory, tested it badly, and stumbled into the history books as the discoverer of lithium in the treatment of manic depression. If he had had a control group of guinea pigs (gave them lithium alone without dissolved urine) he would have found that all his animals flopped on their backs and he would have known then that his theory was incorrect. But then who knows how long it would have taken to discover that lithium works with manic depressives.
  3. Well, poor Sandra did not do well. Her score is 442. The average score is 472, with an average variation or SD of 100. So, we if we translate her score into a z-score then we can find what her percentile is. And if we know her percentile we can figure out how what percent of people score higher.

    4. a z of -.3 corresponds in the normal table on page A-105 to an area of 23.58. That's the center of the z distribution. A -.3 is the (50 - 23.58/2 = ) 38th percentile. So about (100-38 = ) 62% of people scored better than Sandra.

  4. Waldo scored 3 Standard Deviations up from the average on his exam, or about the (50 + 99.73/2 = ) 99th percentile. In contrast Ralph, who had more points, scored only about .5 Standard Deviations up from average or about the (50 + 38.29/2 =) 69th percentile. Waldo appears to have more apptitude than Ralph, if in fact the exams test for the same thing.

5. The first thing to figure out is whether the axis on the left represents percents or counts. Many of you will make the mistake of thinking the numbers on the horizontal axis are percents. They are not. Read the question carefully. In fact, that's a very important thing to do on my exams--read carefully, read everything carefully. The numbers on the bottom are numbers of movies. First figure out the area in the blocks. For example, the left rectangle counts for 10 X 2 = 20 units. Once you count up all the units if they sum to 100, then it's the equivalent of a density histogram and the units on the left axis can be thought of as percents. If not, then the units are counts (like number of people). Find the 75th percentile on the basis of the area in the rectangles.