The Toolkit

10,000 simulated incomes from a lognormal distribution: skewness 3.57, a mean of 49,351 and a median of 36,160. The “average” earner earns less than the average. On a log scale the skewness is 0.0: the data are symmetric in ratios, which is often the right scale to model them on.

• Skewness and kurtosis estimates are dominated by a few extreme points and are unstable in small samples.
• Normality tests reject trivial departures in large samples and miss big ones in small samples; look at a QQ plot instead.
• Transforming the target changes what a model predicts (a median rather than a mean on the original scale).

from scipy.stats import skew
rng = np.random.default_rng(8)
income = rng.lognormal(mean=10.5, sigma=0.8, size=10_000)   # right-skewed, like incomes
stats_raw = (round(skew(income), 2), round(income.mean()), round(np.median(income)))
skew_log = round(skew(np.log(income)), 2)

Assumes import numpy as np and import pandas as pd (and SciPy where imported). Each snippet simulates or makes up its own data, as the comments say.

# Python — distribution diagnostics
from scipy.stats import skew, kurtosis, probplot
import matplotlib.pyplot as plt

print(f"Skew: {skew(data):.3f}")
print(f"Kurt: {kurtosis(data):.3f}")

# QQ plot — points on line = normal
fig, ax = plt.subplots()
probplot(data, plot=ax)
plt.show()