Fall Semester 2002

Lecture Notes Twelve: An Example Midterm Make-Up

Here's an example midterm make-up exam.

1. Consider the following sequence:
`2, 1, 2, 2, 4, 3, 2, 3, 1, 2`
Calculate the mean, mode and the median for this sequence.

2. In the sequence above replace the 4 in the middle with 100. The mean, mode, and the median may change. Calculate the variation for each (new value minus old value) and explain which of the three measures is most sensitive to the change and why? Which is least sensitive and why?

3. A business that designs, manufactures, and sells women's coats needs information on the sizes of its customers. The heights of American women are normally distributed with mean 65 inches and standard deviation 2.5 inches. Assuming that the customers' heights follow a similar distribution, what fraction of the customers will be between 67.5 and 70 inches tall?

4. When are the mean, median, and mode the same value?

5. Probability may be referred to as relative frequency in the long term. Explain what this means. How would you calculate (experimentally, using Excel) the probability of obtaining a 9 when you throw two dice and sum up the values on the faces that come up on the two dice.

6. Larry and Michael have taken two exams:

 Exam Mean Standard Deviation French 85 5 History 88 3
a) Michael got a score of 90 in both. On which did he do better and why?

b) Larry scored 94 on both exams. On which did he do better and why?

Hope this gives you a clear idea of what the exam will be like.

Last updated: Dec 9, 2002 by Adrian German for `A113`