Lower Quartile Calculator

The lower quartile of a data set is a point where about 25% of observations are below that point. It is the middle value between the lowest data point and the median of the data set.

To perform the calculation, enter a series of numbers. Then click the 'Calculate' button.

Input format

The data can be entered as a series of numbers, separated by semicolons or spaces. You can enter the data as a list (one value per line). Or from a column from Excel spreadsheet by copy & paste

Lower Quartile Calculator

Input

Quantile Method

Decimal places

Results

Lower quartile

Quantile Methods

There are several methods for calculating the quartile. Mathematica, Matlab, R and GNU Octave programming languages include nine sample quantile methods.SAS includes five sample quantile methods, SciPy and Maple both include eight, EViews includes the six piecewise linear functions, STATA includes two, and Microsoft Excel includes two. Mathematica supports an arbitrary parameter for methods that allows for other, non-standard, methods.

The calculator above supports the following nine methods:

Default

The default quantile method is identical to type 6

The default method in R, identical to type 7

Maple

The default method in Maple, identical to type 8

Type 1

Inverse of empirical distribution function.
Equivalent to R: 1, SAS: 3, Maple: 1.

Type 2

The same as R-1, but with averaging at discontinuities.
Equivalent to R: 2, SAS: 5, Maple: 2.

Type 3

The observation numbered closest to Np.
Equivalent to R: 3, SAS: 2.

Type 4

Linear interpolation of the empirical distribution function.
Equivalent to R: 4, SAS: 1, SciPy: (0,1), Maple: 3.

Type 5

Piecewise linear function where the knots are the values midway through the steps of the empirical distribution function.
Equivalent to R-5, SciPy-(.5,.5), Maple-4.

Type 6

Linear interpolation of the expectations for the order statistics for the uniform distribution on [0,1]. That is, it is the linear interpolation between points (ph, xh), where ph = h / (N + 1) is the probability that the last of (N+1) randomly drawn values will not exceed the h-th smallest of the first N randomly drawn values.
Equivalent to R-6, Excel, SAS-4, SciPy-(0,0), Maple-5.

Type 7

Linear interpolation of the modes for the order statistics for the uniform distribution on [0,1].
Equivalent to R: 7, Excel, SciPy: (1,1), Maple: 6.

Type 8

Linear interpolation of the approximate medians for order statistics.
Equivalent to R: 8, SciPy: (1/3,1/3), Maple: 7.

Type 9

The resulting quantile estimates are approximately unbiased for the expected order statistics if x is normally distributed.
Equivalent to R: 9, SciPy: (3/8,3/8), Maple: 8.

Lower Quartile Calculator

Calculate the Lower Quartile

Quantile Methods

More Statistics Functions