# 2.9 Practice 2: spread of the data

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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:

• $\mu$ = 1000 FTES
• Median = 1014 FTES
• $\sigma$ = 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

75% of all years have a FTES:

• At or below:
• At or above:

• 1447.5
• 528.5

The population standard deviation =

474 FTES

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

50%

What is the $\mathrm{IQR}$ ? What does the $\mathrm{IQR}$ represent?

919

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

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.

 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

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

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.

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