STATS LAB 5 1 Continuous Distribution Student Learning Outcomes The student will compare and contrast empirical data from a random number generator with the uniform distribution 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 Table 5 3 Calculate the following Organize the Data a a b c d sample mean Sample standard devaton first quartile third quartile median 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 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 ) Describe how changing the number of bars might change the shape Theoretical Distribution In words, X The theoretical distribution of X is X U (0,1) In theory, based upon the distribution X U (0,1), complete the following first quartile third quartile median 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 Construct a box plot of the data Be sure to use a ruler to scale accurately and draw straight edges 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 Q 1 1 5( IQR ) or more than Q 3 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 first quartile median third quartile maximum value width of IQR 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

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STATS LAB 5.1 Continuous Distribution Student Learning Outcomes The student will compare and contrast empirical data from a random number generator with the uniform distribution.

STATS LAB 5.1

Continuous Distribution

Student Learning Outcomes

The student will compare and contrast empirical data from a random number generator with the uniform distribution.

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.

__________

Table 5.3
Calculate the following:

Organize the Data

b. c. d.

sample mean = _________

Sample standard devaton = _______ first quartile = _______

third quartile = _______

median = _______

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

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

Theoretical Distribution

In words, X = _____________________________________.
The theoretical distribution of X is X ~ U(0,1).
In theory, based upon the distribution X ~ U(0,1), complete the following.
= ______
= ______
first quartile = ______
third quartile = ______
median = __________
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

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

first quartile: _______
median: _______
third quartile: _______
maximum value: _______
width of IQR: _______
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?