Quartile

In Statistical descriptive, a quartile is each of the 3 values which divide the data sorted into 4 equal shares, so that each part accounts for 1/4 of the sample of population.

Calculation of the quartiles

See with Quantile for the methods. The quartile is calculated as a 4-quantile. Thus:

  • the 1st quartile separates the 25% inferiors from the data;
  • the 2nd quartile is the median of the series;
  • the 3rd quartile separates the 75% inferiors from the data.

The difference between the 3rd quartile and the 1st quartile is called interquartile variation ; it is a criterion of dispersion of the series.

Method:

  • In the continuous case one uses the function representative of the polygon of the cumulative frequencies. (see with Statistical elementary continuous)
  • In the discrete case one arranges the data by order ascending then: The lower quartile is the value of the medium of the first unit, in which 25% of the values are lower than Q1 and 75% are higher to him. The first quartile takes the Q1 notation. The higher quartile is the value of the medium of the second unit, in which 75% of the values are lower than Q3 and 25% are higher to him. The third quartile thus takes the notation Q3

Example:

Values in the ascending order 1,11,15,19,20,24,28,34,37,47,50,57.

Q1 is between 15 and 19 thus: Q1 = 17

Q2 is between 24 and 28 thus: Q2 = 26 (it is the median )

Q3 is between 37 and 47 thus: Q3 = 42

See too

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