Fall Semester 2002 Answers are in blue

Please answer the questions below:

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.

   The mean is 2.2, the median and mode are equal to 2.

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?

   Without any calculation we should know: mean is most sensitive. The mode won't change. Median might, but slightly in this case (and it doesn't).

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?

   About 13.59% (from mu+sigma to mu+2*sigma)

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

   When the distribution is symmetrical and unimodal (for example normal)

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.

   See Practical Exam One

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?

   Calculate the z scores: French, History.