0.1 Descriptive statistics: descriptive statistics lab (edited:

Descriptive Statistics Lab

Name:

A. student learning objectives

• The student will construct a histogram and a box plot.

• The student will calculate univariate statistics.

• The student will examine the graphs to interpret what the data implies.

B. collect the data

Record the number of pairs of shoes you own:

1. Randomly survey 20 people. Record their values. Survey Results

_____ _____ _____ _____ _____ _____ _____ _____ _____ _____

_____ _____ _____ _____ _____ _____ _____ _____ _____ _____

2. Construct a histogram using Minitab. Choose an appropriate scale and use boundary values (cut points).

3. Calculate the following: Be sure to include the formulas and the appropriate values. Show your work

• $\overline{x}$ =

• s =

4. Are the data discrete or continuous? How do you know? Use complete sentences.

5. Describe the shape of the histogram. Use 2 – 3 complete sentences.

C. analyze the data

1. Determine the following and show your work where appropriate:

• Minimum value =

• Median =

• Maximum value =

• First quartile =

• Third quartile =

• IQR =

2. Using Minitab, construct a box plot of data.

3. What does the shape of the box plot imply about the concentration of data? Use 2 – 3 complete sentences.

4. What does the IQR represent in this problem ? (reference your values)

5. Are there any potential outliers? Which value(s) is (are) it (they)?

Use the formula to calculate the two end values used to determine if a data value is an outlier.

upper =

lower =

6. Show your work to find the value that is 1.5 standard deviations:

a. Above the mean:

b. Below the mean:

c. What percent of the data does Chebyshev’s theorem state lies within 1.5 standard deviations of the mean? (show your work.)

d. What percentage of your data actually falls within 1.5 standard deviations of the mean? How does this compare to the value you calculated in part c above?

7. How does the standard deviation help you to determine concentration of the data and whether or not there are potential outliers?