Question

Use the following information to answer the next nine exercises: The population parameters below describe the full-time equivalent number of students (FTES) each year at Lake Tahoe Community College from 1976–1977 through 2004–2005.

• μ = 1000 FTES

• median = 1,014 FTES

• σ = 474 FTES

• first quartile = 528.5 FTES

• third quartile = 1,447.5 FTES

• n = 29 years

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?

Short answer

The FTES IQR for 1976-77 through 2004-2005 is 919, and the FTES IQR for 2005-2006 through 2010-2011 is 245. As a result, the IQR for the FTES from 1976-77 to 2004-2005 is significantly higher than the IQR for the FTES from 2005-2006 to 2010-2011. Because the number of years covered from 1976-77 to 2004-2005 is 29, and the number of years covered from 2005-2006 to 2010-2011 is 30, they are distinct. In addition, from 2005-2006 to 2010-2011, higher education received additional attention from the FTES.

Step-by-step solution

To find

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?

Explanation

Quartiles are partition variables in statistics that divide data into four equal halves. The first quartile is the value below which 25% of the data is found and above which 75% of the data is found. The median is represented by the second quartile. The third quartile is the value below which 75% of the data is found, and beyond which 25% of the data is found.

The discrepancy between the third and first quartiles is known as the interquartile range. When arranged from lowest to highest, it describes the median 50% of values. IQR is calculated using the following formula:

$IQR=Q_3-Q_1$

The quartiles and interquartile for 1976-77 through 2004-2005 are given below:

$Q_1=528.5,Q_3=1447.5,IQR=919$

The quartiles and interquartile for 2005-2006 through 2010-2011 are given below:

$Q_1=1690,Q_3=1935,IQR=245$

The FTES IQR for 1976-77 through 2004-2005 is 919, and the FTES IQR for 2005-2006 through 2010-2011 is 245. As a result, the IQR for the FTES from 1976-77 to 2004-2005 is significantly higher than the IQR for the FTES from 2005-2006 to 2010-2011. Because the number of years covered from 1976-77 to 2004-2005 is 29, and the number of years covered from 2005-2006 to 2010-2011 is 30, they are distinct. In addition, from 2005-2006 to 2010-2011, higher education received additional attention from the FTES.