21. Stats You Need for Data Work

21.4 Distributions and Skew

By Ravindra Bagale · Last updated: 23 October 2026

In short: Skew is the everyday word for “pulled to one side”.

Why. A histogram answers: are most orders small with a long right tail (festivals), or roughly balanced? Skew is the everyday word for “pulled to one side”.

What.

• Right-skewed (positive): long tail to the right — common for ₹ amounts (many small, few large).
• Left-skewed: long tail to the left — rarer in baskets; sometimes scores.
• Roughly symmetric: mean ≈ median.

You do not need formulas with cubes for this course. Compare mean vs median and look at a histogram.

How.

Worked example A — Normal week vs Ganeshotsav window (fictional Nagpur).

import numpy as np
import pandas as pd

rng = np.random.default_rng(7)
normal = rng.integers(60, 160, size=80)
fest = np.concatenate([
    rng.integers(70, 180, size=70),
    rng.integers(400, 900, size=10),  # mithai / decor spikes
])

def skew_story(arr, label):
    s = pd.Series(arr)
    print(label, "mean", round(s.mean(), 1), "median", s.median(),
          "max", s.max())

skew_story(normal, "Nagpur normal week")
skew_story(fest, "Nagpur Ganeshotsav week")

What you should see. Festival week: mean climbs; median moves less; max jumps. Salman should not staff “average” — he should plan for a fat right tail on festival evenings.

Worked example B — Histogram in five lines.

import matplotlib.pyplot as plt

fig, ax = plt.subplots()
pd.Series(fest).plot(kind="hist", bins=15, ax=ax, edgecolor="black")
ax.set_xlabel("Order amount (₹)")
ax.set_ylabel("Orders")
ax.set_title("Nagpur fictional Ganeshotsav amounts")
fig.savefig("figures/nagpur_fest_hist.png", dpi=120, bbox_inches="tight")
plt.close()

Save the PNG for WhatsApp (Chapter 22). Do not paste the whole notebook.

Worked example C — Status mix is also a “distribution”.

status = pd.Series(
    ["Delivered"] * 50 + ["Cancelled"] * 6 + ["Returned"] * 4
)
print(status.value_counts(normalize=True).round(3))

Zoya reports: “Delivered 83%, Cancelled 10%, Returned 7% (fictional sample).” That categorical distribution matters as much as ₹ skew.