2.8 Descriptive statistics -- rrc math1020

Descriptive statistics

Class Time:

Names:

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

1. Randomly survey 30 classmates about the number of pairs of shoes they own. Record their values.

   Survey results

   _____	_____	_____	_____	_____
   _____	_____	_____	_____	_____
   _____	_____	_____	_____	_____
   _____	_____	_____	_____	_____
   _____	_____	_____	_____	_____
   _____	_____	_____	_____	_____

2. Construct a histogram. Make five to six intervals. Sketch the graph using a ruler and pencil and scale the axes.

   

3. Calculate the following values.
   1. $\overline{x}$ = _____
   2. s = _____
4. Are the data discrete or continuous? How do you know?
5. In complete sentences, describe the shape of the histogram.
6. 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

1. Determine the following values.
   1. Min = _____
   2. M = _____
   3. Max = _____
   4. Q ₁ = _____
   5. Q ₃ = _____
   6. IQR = _____
2. Construct a box plot of data
3. What does the shape of the box plot imply about the concentration of data? Use complete sentences.
4. Using the box plot, how can you determine if there are potential outliers?
5. How does the standard deviation help you to determine concentration of the data and whether or not there are potential outliers?
6. What does the IQR represent in this problem?
7. Show your work to find the value that is 1.5 standard deviations:
   1. above the mean.
   2. below the mean.