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Practice 2: Spread of the Data

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

Summary: 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:

  • μμ = 1000 FTES
  • Median = 1014 FTES
  • σσ = 474 FTES
  • First quartile = 528.5 FTES
  • Third quartile = 1447.5 FTES
  • nn = 29 years

Calculate the Values

Exercise 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.

Solution

6

Exercise 2

75% of all years have a FTES:

  • a. At or below:
  • b. At or above:

Solution

  • a. 1447.5
  • b. 528.5

Exercise 3

The population standard deviation =

Solution

474 FTES

Exercise 4

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

Solution

50%

Exercise 5

What is the IQRIQR? What does the IQRIQR represent?

Solution

919

Exercise 6

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

Solution

0.03

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.

Table 1
Year 2005-06 2006-07 2007-08 2008-09 2009-10 2010-11
Total FTES 1585 1690 1735 1935 2021 1890

Exercise 7

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

Solution

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

Exercise 8

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

Exercise 9

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?

Solution

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

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