<< Chapter < Page Chapter >> Page >
Practice exercise for Descriptive Statistics

Student learning outcomes

  • The student will calculate measures of the center of the data.
  • The student will calculate the spread of the data.

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:

  • μ = 1000 FTES
  • Median = 1014 FTES
  • σ = 474 FTES
  • First quartile = 528.5 FTES
  • Third quartile = 1447.5 FTES
  • n = 29 years

Calculate the values

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.

6

Got questions? Get instant answers now!

75% of all years have a FTES:

  • At or below:
  • At or above:

  • 1447.5
  • 528.5
Got questions? Get instant answers now!

The population standard deviation =

474 FTES

Got questions? Get instant answers now!

What percent of the FTES were from 528.5 to 1447.5? How do you know?

50%

Got questions? Get instant answers now!

What is the IQR ? What does the IQR represent?

919

Got questions? Get instant answers now!

How many standard deviations away from the mean is the median?

0.03

Got questions? Get instant answers now!

Additional Information: The population FTES for 2005-2006 through 2010-2011 was given in an updated report. (Source: http://www.ltcc.edu/data/ResourcePDF/LTCC_FactBook_2010-11.pdf). The data are reported here.

Year 2005-06 2006-07 2007-08 2008-09 2009-10 2010-11
Total FTES 1585 1690 1735 1935 2021 1890

Calculate the mean, median, standard deviation, first quartile, the third quartile and the IQR. Round to one decimal place.

mean = 1809.3
median = 1812.5
standard deviation = 151.2
First quartile = 1690
Third quartile = 1935
IQR = 245

Got questions? Get instant answers now!

Construct a boxplot for the FTES for 2005-2006 through 2010-2011 and a boxplot for the FTES for 1976-1977 through 2004-2005.

Got questions? Get instant answers now!

Compare the IQR for the FTES for 1976-77 through 2004-2005 with the IQR for the FTES for 2005-2006 through 2010-2011. Why do you suppose the IQRs are so different?

Hint: Think about the number of years covered by each time period and what happened to higher education during those periods.

Got questions? Get instant answers now!

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play Download on the App Store Now




Source:  OpenStax, Collaborative statistics. OpenStax CNX. Jul 03, 2012 Download for free at http://cnx.org/content/col10522/1.40
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Collaborative statistics' conversation and receive update notifications?

Ask