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

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

Short answer

Because these values are the first and third quartiles, and we know that 50% of the FTES are inside this range, 50% of the FTES were between 528.5 and 1447.5.

Step-by-step solution

To find

What percent of the FTES were from 528.5 to 1447.5

Explanation

The median is a number that divides the data into two equal halves and is one of the measures of central tendency in statistics. The data in the 50% range is below the median value while the data in the 50% range is above the median value.

The partition values that divide the data into four equal halves are called quartiles. 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.

We also know that between the first and third quartiles, there is 50%of data.

In the given example, we are given the below parameters about the population:

$$\begin{gathered} \mu =1000\mathrm{FTES} \\ median=1014FTES \\ \sigma =474FTES \\ firstquartile=528.5\mathrm{FTES} \\ thirdquartile=1447.5FTES \\ n=29years \end{gathered}$$

Since 528.5 denotes the first quartile and 1447.5 denotes the third quartile, therefore, there will be 50 % of the FTES from 528.5 to 1447.5

Therefore These values are the first and third quartiles, so 50% of the FTES are within this range.