Variability of data

The goal of this lab is to compute the standard deviation of a data set and to see how this information relates to the shape of the distribution. Remember to state your answers in writing.

PROBLEM 1. The mathematics SAT scores of 100 students have been classified below using intervals of size 50.

Interval Number Mid-point
400-449 2 425
450-499 3 475
500-549 9 525
550-599 19 575
600-649 29 625
650-699 16 675
700-749 18 725
750-800 4 775

Compute the mean SAT score and the standard deviation. (Hint: place the intervals in column A - the range A4..A11 will do. Place the "midpoints" in column C and then the number (ie., frequency) in column B. Compute the mean (xBar) as in the lab on distribution means. To calculate the standard deviation, first find the variance. To do this make a column for freq*(x-xBar)^2. Then find the sum and divide by the population size (or sample size minus one) .

PROBLEM 2. In the next term a student plans to take an English class and has a choice of Instructor A or Instructor B. Below is a record of the last 100 grades given by each instructor.

F D C B A
Instructor A: 31 18 6 10 35
Instructor B: 1 25 47 27 0

Place the grade data for Instructor A in column A and the data for Instructor B in column B.

a. Compute the mean of each instructor's grades. ( You should add a third column with the values 0, 1, 2, 3, and 4 to represent the numerical value of each grade.)

b. Compute the standard deviation of each instructor's grades.

c. Analyze the grade data with a histogram (column graph). You may use either the letters or the letter grades for the X-range.

d. Write a paragraph to discuss each instructor based on the features of the grade distribution. With which instructor is there the greatest risk of failing? If you are an A student, explain which instructor you would choose and why. If you are a D student explain which instructor you would choose and why. Think up two questions stimulated by your analysis of the grades.