# 2.9: Descriptive Statistics (Worksheet)

Name: ______________________________

Section: _____________________________

Student ID#:__________________________

*Work in groups on these problems. You should try to answer the questions without referring to your textbook. If you get stuck, try asking another group for help.*

### Student Learning Outcomes

- 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.

### Collect the Data

Record the number of pairs of shoes you own.

- Randomly survey 30 classmates about the number of pairs of shoes they own. Record their values.
*Survey Results*_____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____ - Construct a histogram. Make five to six intervals. Sketch the graph using a ruler and pencil and scale the axes.
**Figure 2.9.1** - Calculate the following values.
- \(\bar{x}\) = _____
- \(s\) = _____

- Are the data discrete or continuous? How do you know?
- In complete sentences, describe the shape of the histogram.
- Are there any potential outliers? List the value(s) that could be outliers. Use a formula to check the end values to determine if they are potential outliers.

### Analyze the Data

- Determine the following values.
- Min = _____
*M*= _____- Max = _____
*Q*_{1}= _____*Q*_{3}= _____*IQR*= _____

- Construct a box plot of data
- What does the shape of the box plot imply about the concentration of data? Use complete sentences.
- Using the box plot, how can you determine if there are potential outliers?
- How does the standard deviation help you to determine concentration of the data and whether or not there are potential outliers?
- What does the
*IQR*represent in this problem? - Show your work to find the value that is 1.5 standard deviations:
- above the mean.
- below the mean.