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Descriptive Statistics: Practice

Module by: Barbara Illowsky, Ph.D., Susan Dean. E-mail the authors

Summary: This module provides students with opportunities to apply concepts related to descriptive statistics. Students are asked to take a set of sample data and calculate a series of statistical values for that data. Note: This module is currently under revision, and its content is subject to change. This module is being prepared as part of a statistics textbook that will be available for the Fall 2008 semester.

Note: You are viewing an old version of this document. The latest version is available here.

Student Learning Outcomes

  • The student will calculate and interpret the center, spread, and location of the data.
  • The student will construct and interpret histograms an box plots.

Given

Sixty-five randomly selected car salespersons were asked the number of cars they generally sell in one week. Fourteen people answered that they generally sell three cars; nineteen generally sell four cars; twelve generally sell five cars; nine generally sell six cars; eleven generally sell seven cars.

Complete the Table

Table 1
Data Value (# cars) Frequency Relative Frequency Cumulative
       
       
       
       
       
       
       

Discussion Questions

  1. What does the frequency column sum to? Why?
  2. What does the relative frequency column sum to? Why?
  3. What is the difference between relative frequency and frequency for each data value?
  4. What is the difference between cumulative relative frequency and relative frequency for each data value?

Enter the Data

Enter your data into your calculator or computer.

Construct a Histogram

Determine appropriate minimum and maximum x and y values and the scaling. Sketch the histogram below. Label the horizontal and vertical axes with words. Include numerical scaling.

graph1.png

Data Statistics

Calculate the following values:

  • Sample mean = x¯ x =
  • Sample standard deviation = sx s x =
  • Sample size = n =

Calculations

Use the table above to calculate the following values:

  1. Median =
  2. Mode =
  3. First quartile =
  4. Second quartile = median = 50th percentile =
  5. Third quartile =
  6. Interquartile range (IQRIQR) = _____ - _____ = _____
  7. 10th percentile =
  8. 70th percentile =
  9. Find the value that is 3 standard deviations:
    • Above the mean
    • Below the mean

Box Plot

Construct a box plot below. Use a ruler to measure and scale accurately.

Interpretation

Looking at your box plot, does it appear that the data are concentrated together, spread out evenly, or concentrated in some areas, but not in others? How can you tell?

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