In descriptive statistics, a quartile is one of three points, that divide a data set into four equal groups, each representing a fourth of the distributed sampled population. It is a type of quantile.
In epidemiology, the four ranges defined by the three values discussed here.
Contents
Definitions
 first quartile (designated Q_{1}) = lower quartile = cuts off lowest 25% of data = 25th percentile
 second quartile (designated Q_{2}) = median = cuts data set in half = 50th percentile
 third quartile (designated Q_{3}) = upper quartile = cuts off highest 25% of data, or lowest 75% = 75th percentile
The difference between the upper and lower quartiles is called the interquartile range.
Computing methods
There is no universal agreement on choosing the quartile values.^{[1]}
One standard formula for locating the position of the observation at a given percentile, y, with n data points sorted in ascending order is:^{[2]}
 Case 1: If L is a whole number, then the value will be found halfway between positions L and L+1.
 Case 2: If L is a decimal, round to the nearest whole number. (for example, L = 1.2 becomes 1).
Example
Method 1
This rule is employed by the TI83 calculator boxplot and 1Var Stats functions.
Method 2
Example 1
Data Set: 6, 47, 49, 15, 42, 41, 7, 39, 43, 40, 36
Ordered Data Set: 6, 7, 15, 36, 39, 40, 41, 42, 43, 47, 49
Example 2
Ordered Data Set: 7, 15, 36, 39, 40, 41
Example 3
Ordered Data Set: 1, 2, 3, 4
First Quartile can be calculated by the following formula if (n+1)/4 the value is not an integer. Let us consider the case that we might have 12 observations i.e. n=12 then Q1=(12+1)/4 the value i.e. Q1=3.25th value. To find the 3.25 the value we can use the formula Q1= 3rd value + 0.25 [4th value  3rd value] same procedure can be adopted for any fractional value of Q1 and Q3.
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