Quartile

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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 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.

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 TI-83 calculator boxplot and 1-Var 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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