One Number To Stand For Manyबहुत सारे Numbers के लिए एक Number用一个数代表一堆数

Understand It Before the Mathsगणित से पहले समझें先看懂，再学公式

The Three Measures At A Glanceतीनों Measures एक नज़र में三种度量一览

The Mean — Every Value Gets A VoteMean — हर Value को एक Vote均值 — 每个值都有一票

One Outlier Can Break The Meanएक Outlier Mean को बिगाड़ सकता है一个离群点就能“打破”均值

import numpy as np

# Monthly salaries (₹) of a 10-person team
team = [32000, 35000, 38000, 40000, 41000, 43000, 44000, 46000, 47000, 54000]
print(f"Team only  → mean ₹{np.mean(team):,.0f}   median ₹{np.median(team):,.0f}")

# Add the CEO's salary
with_ceo = team + [500000]
print(f"With CEO   → mean ₹{np.mean(with_ceo):,.0f}   median ₹{np.median(with_ceo):,.0f}")

jump = (np.mean(with_ceo) / np.mean(team) - 1) * 100
print(f"The mean jumped {jump:.0f}%; the median moved only ₹{np.median(with_ceo) - np.median(team):,.0f}")

The Median — The True MiddleMedian — असली बीच中位数 — 真正的中间

The Mode — What Shows Up MostMode — जो सबसे ज़्यादा दिखे众数 — 出现最多的

Outliers — The Mean Moves, The Median HoldsOutliers — Mean हिलता है, Median टिका रहता है离群点 — 均值会动，中位数稳住

How Skew Reorders The ThreeSkew तीनों का क्रम कैसे बदलता है偏斜如何改变三者的顺序

The Mean–Median Gap Measures SkewMean–Median Gap, Skew को मापता है均值与中位数之差反映偏斜

Which Measure, When?कौन सा Measure, कब?什么时候用哪个？

Pick The Right Measureसही Measure चुनें选出合适的度量

All Three On 20 Exam Scores20 Exam Scores पर तीनों用 20 个考试分数算三者

Twenty students score between 45 and 92. Their scores add up to 1,369, and 65 appears three times.

बीस students के scores 45 से 92 के बीच हैं। उनका जोड़ 1,369 है, और 65 तीन बार आता है।

二十名学生的分数在 45 到 92 之间，总分 1,369，其中 65 出现了三次。

Computing All Three In PythonPython में तीनों निकालना用 Python 计算三者

import numpy as np
from scipy import stats

# All 20 exam scores (no "..." — this list is complete)
scores = [45, 52, 55, 57, 60, 61, 62, 63, 64, 65,
          65, 65, 70, 73, 76, 80, 85, 88, 91, 92]

mean   = np.mean(scores)
median = np.median(scores)
mode   = stats.mode(scores, keepdims=False)    # returns (mode, count)

print("Count :", len(scores), "  Sum:", sum(scores))
print("Mean  :", mean)
print("Median:", median)
print("Mode  :", mode.mode, f"(appears {mode.count} times)")

# The mean–median gap is a quick skewness check
gap = mean - median
if abs(gap) < 0.5:
    print("Roughly symmetric")
else:
    print("Right-skewed" if gap > 0 else "Left-skewed", f"(gap = {gap:+.2f})")
print("Skewness (scipy):", round(stats.skew(scores), 3))

In pandas It Is One Call Eachpandas में हर एक के लिए एक Call在 pandas 中各需一行

# Continues from the previous slide (uses the same `scores` list)
import pandas as pd

df = pd.DataFrame({'score': scores})
df['grade'] = pd.cut(df['score'], bins=[0, 54, 69, 84, 100],
                     labels=['C', 'B', 'A', 'A+'])

print(df['score'].mean(), df['score'].median(), df['score'].mode().tolist())
print(df['grade'].value_counts().sort_index().to_dict())
print("Most common grade:", df['grade'].mode()[0])   # mode works on categories too
print(df['score'].describe().round(2))               # the 50% row is the median

Central Tendency In The Real Worldअसली दुनिया में Central Tendency现实世界中的集中趋势

Six Rules That Keep You Honestछह नियम जो आपको ईमानदार रखते हैं让你保持诚实的六条规则

Three Measures, One Clear Pictureतीन Measures, एक साफ़ तस्वीर三种度量，一幅清晰的图景