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Reproducible example

from datetime import date
import polars as pl

s = pl.Series([date(2024, 1, 1), date(2024, 1, 2)])
print("mean:")
print(s.mean())
print(s.dt.mean())
print(s.to_frame().select(pl.all().mean()))

print("\nmedian:")
print(s.median())
print(s.dt.median())
print(s.to_frame().select(pl.all().median()))

Log output

mean:
19723.5
2024-01-01
shape: (1, 1)
┌──────┐
│      │
│ ---  │
│ date │
╞══════╡
│ null │
└──────┘

median:
19723.5
2024-01-01
polars.exceptions.InvalidOperationError: `median` operation not supported for dtype `date`

Issue description

dt.mean() returns a date and mean() returns a float or null, depending on context, when the input has dtype pl.Date. Median similarly has inconsistent behavior.

Using the analogy for integers and real numbers, the mean and median of dates should be a datetime, similar to how the mean and median of an integers is a float:

mean(1, 2) = 1.5
mean(2024-01-01, 2024-01-02) = 2024-01-01 12:00:00

Expected behavior

Returns a datetime that is at the average (mean or median) time point, and is consistent across uses of mean and median.

Implementing this for the remaining temporal types (in a future issue) will enable the deprecation of .dt.mean and .dt.median, as those will become redundant with series.mean and series.median when the datatype is temporal.

Installed versions

--------Version info---------
Polars:               0.20.3
Index type:           UInt32
Platform:             Windows-10-10.0.22621-SP0
Python:               3.11.4 (tags/v3.11.4:d2340ef, Jun  7 2023, 05:45:37) [MSC v.1934 64 bit (AMD64)]

----Optional dependencies----
adbc_driver_manager:  <not installed>
cloudpickle:          3.0.0
connectorx:           0.3.2
deltalake:            0.15.1
fsspec:               2023.12.2
gevent:               23.9.1
hvplot:               0.9.1
matplotlib:           3.8.2
numpy:                1.26.3
openpyxl:             3.1.2
pandas:               2.1.4
pyarrow:              14.0.2
pydantic:             2.5.3
pyiceberg:            0.5.1
pyxlsb:               1.0.10
sqlalchemy:           2.0.25
xlsx2csv:             0.8.1
xlsxwriter:           3.1.9