Collect the Data: Use a random number generator or your calculator to generate 50 values between zero

and one (inclusive). You may need to review secton1.2 List them below. Round the numbers to four

decimal places or set the calculator MODE to four places.

1. Complete the table.

__________ __________ __________ __________ __________

__________ __________ __________ __________ __________

__________ __________ __________ __________ __________

__________ __________ __________ __________ __________

__________ __________ __________ __________ __________

__________ __________ __________ __________ __________

__________ __________ __________ __________ __________

__________ __________ __________ __________ __________

__________ __________ __________ __________ __________

__________ __________ __________ __________ __________

2. Table 5.3

3. Calculate the following:

a. sample mean = _________

a. Sample standard devaton = _______

b. first quartile = _______

c. third quartile = _______

d. median = _______

Organize the Data

1. Construct a histogram of the empirical data. Make eight bars.

Figure 5.33

2. Construct a histogram of the empirical data. Make five bars.

Figure 5.34

Describe the Data

1. In two to three complete sentences, describe the shape of each graph. (Keep it simple. Does the graph

go straight across, does it have a V shape, does it have a hump in the middle or at either end, and so on.

One way to help you determine a shape is to draw a smooth curve roughly through the top of the bars.)

2. Describe how changing the number of bars might change the shape.

Theoretical Distribution

1. In words, X = _____________________________________.

2. The theoretical distribution of X is X ~ U(0,1).

3. In theory, based upon the distribution X ~ U(0,1), complete the following.

a. = ______

b. = ______

c. first quartile = ______

d. third quartile = ______

e. median = __________

4. Are the empirical values (the data) in the section titled Collect the Data close to the corresponding

theoretical values? Why or why not?

Plot the Data

1. Construct a box plot of the data. Be sure to use a ruler to scale accurately and draw straight edges.

2. Do you notice any potential outliers? If so, which values are they? Either way, justify your answer

numerically. (Recall that any DATA that are less than Q1 - 1.5(IQR) or more than Q3 + 1.5(IQR) are

potential outliers. IQR means interquartile range.)

Compare the Data

1. For each of the following parts, use a complete sentence to comment on how the value obtained from

the data compares to the theoretical value you expected from the distribution in the section

titled Theoretical Distribution.

a. minimum value: _______

b. first quartile: _______

c. median: _______

d. third quartile: _______

e. maximum value: _______

f. width of IQR: _______

g. overall shape: _______

2. Based on your comments in the section titled Collect the Data, how does the box plot fit or not fit what

you would expect of the distribution in the section titled Theoretical Distribution?

Discussion Question

1. Suppose that the number of values generated was 500, not 50. How would that affect what you would

expect the empirical data to be and the shape of its graph to look like?