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.
- first quartile (designated Q1) = lower quartile = cuts off lowest 25% of data = 25th percentile
- second quartile (designated Q2) = median = cuts data set in half = 50th percentile
- third quartile (designated Q3) = 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.
There is no universal agreement on choosing the quartile values.
One standard formula for locating the position of the observation at a given percentile, y, with n data points sorted in ascending order is:
- 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).
This rule is employed by the TI-83 calculator boxplot and 1-Var Stats functions.
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
Ordered Data Set: 7, 15, 36, 39, 40, 41
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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