Lists

14.5.1 Lists

The functions described here can be used if a statistics series is contained in a list. See Section 14.5.2 for statistics on matrices and Section 20 for more general statistics.

Let L be a list.

mean(L) computes the arithmetic mean of a list.
stddev(L) computes the standard deviation of a population, for the population L.
stddevp(L) computes an unbiased estimate of the standard deviation of the population for the sample L. The following relation holds:
stddevp(L)²=
size(L)·stddev(L)²

size(L)−1
variance(L) computes the variance of L, which is the square of stddevp(L).
median(L) computes the median of L.
quantile(L,d) computes the deciles of L, where d is the decile.
quartiles(L) returns a list consisting of the minimum, the first quartile, the median, the third quartile and the maximum of L.
boxwhisker(L) draws the whisker box of a statistics series stored in L.

Examples

mean([3,4,2])

stddev([3,4,2])

√

stddevp([3,4,2])

variance([3,4,2])

median([0,1,3,4,2,5,6])

3.0

To obtain the first quartile:

quantile([0,1,3,4,2,5,6],0.25)

1.0

To obtain the median:

quantile([0,1,3,4,2,5,6],0.5)

3.0

To obtain the third quantile:

quantile([0,1,3,4,2,5,6],0.75)

5.0

quartiles([0,1,3,4,2,5,6])

⎡
⎢
⎢
⎢
⎢
⎢
⎣

0.0

1.0

3.0

5.0

6.0

⎤
⎥
⎥
⎥
⎥
⎥
⎦

boxwhisker([0,1,3,4,2,5,6])