A quartile of a sorted data set is any of the three values that divide the data set into four equal parts; the upper quartile identifies the 1/4 of the population members that have the highest value. This term is used extensively in pure statistics, but also has applications in fields that use statistics, such as epidemiology. It is important to note that there is no specific rule for choosing the quartile values, although several techniques are common.

Define the upper quartile more formally. The upper quartile may also be called the third quartile and is frequently designated as Q3. Since it separates the highest 25 percent of the data from the lowest 75 percent, it may also be identified as the 75th percentile.

Examine the problem with assigning an exact value for the upper quartile. This revolves around the issue of how to assign the quartile value when the number of members in the population is not divisible by four. For example, if the population has five members, the upper fourth of the population may or may not include the fourth member.

Examine one common method for evaluating percentiles. This may be expressed as V = (n+1)(y/100), where V is the value that separates the bottom y percent of the population from the top (100 - y) percent of the population. If V is a whole number, population elements with a value of V belong in the upper range.

Evaluate the method given in step 3 for the upper quartile. Given the equation V = (n+1)(y/100), we use y=75, since the upper quartile also represents the 75th percentile. This gives us V = (n+1)(y/100) = (n+1)(75/100) = (n+1)(3/4) = (3n+3)/4.

Find the upper quartile for a population of 5 members. We have V = (3n+3)/4 = (3x5+3)/4 = (15+3)/4 = 18/4 = 4.5. The upper quartile is 4.5, so the upper fourth of the population will only include members with a ranking higher than 4.5. Therefore, the upper fourth of this population will consist only of the fifth member using the method described in Step 3.

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