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Descriptive Statistics: Practice

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

Summary: 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.

Practice 1:

Calculating & interpreting the center, spread & location of data constructing & interpreting histograms and 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 your data into your computer or calculator

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.JPG

Data Statistics

sample mean = x¯ x = __________

sample standard deviation = sx s x = _________

sample size = n = __________

Use the table on the first page of this practice to answer the following

  1. median = _________
  2. mode = ___________
  3. fist quartile = ___________
  4. second quartile = median = 50th percentile = _____________
  5. third quartile = _____________
  6. interquartile range (IQR) = ____________________ - ________________ = ________________
  7. 10th percentile = _______________
  8. 70th percentile = _______________
  9. Find the value that is 3 standard deviations: a. above the mean ______________ b. below the mean _____________

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?

Practice 2:

Understanding theoretical symbols

Given

The population parameters below describe the full-time equivalent number of students (FTES) each year at Lake Tahoe Community College from 1976-77 through 2004-2005. (Source: Graphically Speaking by Bill King, LTCC Institutional Research, December 2005). Use these values to answer the following questions:

  • μμ = 1000 FTES
  • median - 1014 FTES
  • σσ = 474 FTES
  • first quartile = 528.5 FTES
  • third quartile = 1447.5 FTES
  • n = 29 years
  1. A sample of 11 years is taken. About how many are expected to have a FTES of 1014 or above? Explain how you determined your answer _____________________________________________________
  2. 75% of all years have a FTES: a) at or below _______________________ b) at or above _________________
  3. The population standard deviation = _______________________
  4. What percent of the FTES were from 528.5 to 1447.5? _______________________ How do you know?
  5. What pis the IQR? ____________________ What does the IQR represent?
  6. How many standard deviations away from the mean is the median? ____________

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