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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鈥1977 through 2004鈥2005.

鈥 渭 = 1000 FTES

鈥 median = 1,014 FTES

鈥 蟽 = 474 FTES

鈥 first quartile = 528.5 FTES

鈥 third quartile = 1,447.5 FTES

鈥 n = 29 years

75% of all years have an FTES:

a. at or below: _____

b. at or above: _____

Short Answer

Expert verified

75% of all years have an FTES:

a. At or below 1447.5

b. At or above 528.5

Step by step solution

01

To find

75 % of all years have an FTES:

a. At or below

b. At or above

02

Explanation

The median is a number that splits 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.

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

=1000FTESmedian=1014FTES=474FTESfirstquartile=528.5FTESthirdquartile=1447.5FTESn=29years

We must determine the 75% of all years with an FTES at or below a certain value, as well as the 75% of all years with an FTES at or above a certain value.

We know that 75% of data falls below the third quartile figure, thus we have: 75% of all years with an FTES of 1447.5 or less.

We also know that 75% of data is above the first quartile value, so we have: 75% of all years with an FTES of 528.5 or above.

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