5.6-dars: Box plot

5-QISM — VIZUALIZATSIYA · 6-dars

1. Kirish va motivatsiya

Box plot (quti diagramma) — taqsimotni beshtalik xulosa 4.4-bob bilan ixcham ko'rsatuvchi grafik: median, kvartillar (Q1, Q3), va outlier'lar. Quti Q1 dan Q3 gacha (o'rta 50%), ichidagi chiziq — median, "mo'ylovlar" (whiskers) — asosiy diapazon, chetdagi nuqtalar — outlier. Box plot histogramdan kamroq detal beradi, lekin guruhlarni taqqoslashda tengsiz: 10 shahar maoshini yonma-yon (10 quti) — median, tarqoqlik, outlier bir qarashda. Nega muhim? (1) Ixcham taqsimot — 5 son (median, kvartil, outlier); (2) Guruh taqqoslash — ko'p quti yonma-yon; (3) Outlier — chetdagi nuqtalar aniq. Bu dars box plotni chuqur o'rgatadi — taqsimotni ixcham ko'rsatish va taqqoslash.

Box plot — taqsimot beshtalik xulosa: ax.boxplot (quti — Q1/median/Q3/mo'ylov/outlier), beshtalik xulosa (min, Q1, median, Q3, max — 4.4), quti (Q1-Q3 — o'rta 50%, IQR), mo'ylov (whisker — asosiy diapazon, 1.5*IQR), outlier (chetdagi nuqta), guruh taqqoslash (ko'p quti yonma-yon). Foydalanish: ixcham taqsimot, guruh taqqoslash, outlier. Bu 4.4 (kvartil), 5.5 (histogram) bilan bog'liq. Box plot — beshtalik xulosa. Guruh. Outlier.

Real vaziyat. Data Scientist 10 shahar maoshini taqqosladi: ax.boxplot([shahar1, shahar2, ...]) — har shahar bir quti (median chiziq — o'rta maosh; quti — o'rta 50%; mo'ylov — diapazon; nuqtalar — outlier). Bir qarashda: Toshkent median yuqori (chiziq baland), tarqoqlik katta (quti keng); ba'zi shaharda outlier (juda yuqori maosh — direktor). Histogram (bir shahar — detal shakl) vs box plot (10 shahar — taqqoslash, ixcham). Outlier (chetdagi nuqta — 1.5*IQR, 4.4). Box plot guruhlarni taqqosladi (median/tarqoqlik/outlier — bir qarashda). Box plot — taqqoslash ko'zi (ixcham, guruh).

Bu darsda box plotni o'rganamiz.

Bu darsda:

• Box plot (boxplot)
• Box plot qismlari (quti, mo'ylov, outlier)
• Guruh taqqoslash
• Box plot vs histogram
• Outlier ko'rsatish
• Box plot amaliyoti
• Box plot tuzoqlari
• Amaliy: box plot modeli

ℹ Misollar real matplotlib/numpy bilan (Agg — grafik xususiyatlari matn bilan tekshiriladi) ishlaydi.

2. Nazariya — chuqur tushuntirish

2.1. Box plot (boxplot)

Taqsimot 5 son bilan:

import matplotlib.pyplot as plt
import numpy as np

np.random.seed(0)
data = np.random.normal(50, 15, 200)

fig, ax = plt.subplots()
ax.boxplot(data)     # quti: Q1/median/Q3/mo'ylov/outlier

ax.set_ylabel("Qiymat")

Box plot (boxplot) — taqsimot beshtalik xulosa: ax.boxplot(data) (quti — median, kvartillar (Q1/Q3), mo'ylov, outlier; 4.4 beshtalik xulosa). Sabab: taqsimotni ixcham ko'rsatish (5 son — median markaz, kvartil tarqoqlik, outlier chet; histogram — detal, box plot — ixcham); guruh taqqoslash (ko'p quti — bir qarashda). ax.boxplot(data) (bir quti) yoki ax.boxplot([a, b, c]) (ko'p — taqqoslash). Box plot beshtalik xulosani vizual (4.4 — min/Q1/median/Q3/max). Box plot — boxplot (beshtalik xulosa). Ixcham. Guruh.

2.2. Box plot qismlari

Quti, mo'ylov, outlier:

BOX PLOT QISMLARI:
   ┬  ← yuqori mo'ylov (Q3 + 1.5*IQR gacha)
   │
  ┌─┐ ← Q3 (75%)
  │ │ ← QUTI (o'rta 50% — IQR)
  ├─┤ ← MEDIAN (50% — o'rta chiziq)
  │ │
  └─┘ ← Q1 (25%)
   │
   ┴  ← past mo'ylov (Q1 - 1.5*IQR gacha)
   o  ← OUTLIER (mo'ylovdan tashqari — chetdagi nuqta)

Box plot qismlari — quti, mo'ylov, outlier: quti (box — Q1 dan Q3 gacha, o'rta 50% — IQR 4.4), median chiziq (quti ichida — 50%, markaz), mo'ylov (whisker — quti'dan chiziqlar; asosiy diapazon — 1.5*IQR gacha), outlier (mo'ylovdan tashqari — chetdagi nuqta, 4.4). Sabab: box plot beshtalik xulosani ko'rsatadi (quti — kvartil/IQR; median — markaz; mo'ylov — diapazon; outlier — chet); har qism ma'no (quti balandlik — tarqoqlik; median joyi — markaz; outlier — chet). Box plot qismlari — quti (Q1-Q3), median, mo'ylov (1.5*IQR), outlier. Beshtalik. Qism.

2.3. Guruh taqqoslash

Ko'p quti yonma-yon:

import matplotlib.pyplot as plt
import numpy as np

np.random.seed(0)
shahar1 = np.random.normal(500, 100, 200)
shahar2 = np.random.normal(400, 80, 200)
shahar3 = np.random.normal(600, 150, 200)

fig, ax = plt.subplots()
ax.boxplot([shahar1, shahar2, shahar3], tick_labels=["T", "S", "B"])

# har shahar — bir quti (median, tarqoqlik, outlier taqqoslash)

Guruh taqqoslash — ko'p quti yonma-yon: ax.boxplot([a, b, c], tick_labels=[...]) (har guruh bir quti — yonma-yon; taqqoslash). Sabab: box plot eng kuchli guruh taqqoslashda (10 shahar maoshi — 10 quti; median/tarqoqlik/outlier bir qarashda); histogram (bir taqsimot — detal; ko'p — chalkash 5.5); box plot ixcham (ko'p guruh — yonma-yon, aniq). Taqqoslash: median (chiziq balandlik — qaysi katta), tarqoqlik (quti kengligi — qaysi keng), outlier (chet — qaysi). Guruh taqqoslash — ko'p quti (yonma-yon). Ixcham. Bir qarashda.

2.4. Box plot vs histogram

Box plot vs histogram — qachon qaysi: histogram (bir taqsimot — detal shakl: bimodal, aniq shakl; bir/ikki o'zgaruvchan), box plot (ixcham — 5 son: median/kvartil/outlier; guruh taqqoslash — ko'p yonma-yon). Sabab: turli maqsad — shakl detal (histogram — bimodal ko'rinadi; box plot bimodalni yashiradi — faqat median/kvartil), taqqoslash (box plot — ko'p guruh yonma-yon; histogram — 2-3 chalkash). Box plot kamchiligi: shakl detal yo'q (bimodal — box plot bir xil ko'rsatadi; histogram kerak). Box plot (taqqoslash, ixcham, outlier), histogram (shakl detal, bir taqsimot). Box plot vs histogram — ixcham/taqqoslash vs detal shakl. Qachon qaysi. Maqsad.

2.5. Outlier ko'rsatish

Outlier ko'rsatish — chetdagi nuqta: box plot outlierni avtomatik ko'rsatadi (mo'ylovdan tashqari — Q1-1.5*IQR past yoki Q3+1.5*IQR yuqori; 4.4; alohida nuqta). Sabab: box plot outlier aniqlash uchun ideal (IQR usuli — 4.4; chetdagi nuqta avtomatik); guruh outlier (ko'p quti — qaysi guruhda outlier). whis (mo'ylov uzunligi — standart 1.5; o'zgartirish mumkin). Outlier tekshirish (box plot — ko'r; xato yoki maxsus holat — tozalash 6-qism). Box plot outlier + taqsimot (bir grafikda). Outlier ko'rsatish — chetdagi nuqta (avtomatik, 1.5*IQR). Outlier. IQR.

2.6. Box plot amaliyoti

Box plot amaliyoti: ax.boxplot (beshtalik xulosa); qismlar (quti Q1-Q3, median, mo'ylov, outlier); guruh taqqoslash (ko'p quti — tick_labels); vs histogram (ixcham/taqqoslash vs detal); outlier (avtomatik — 1.5*IQR); Pandas/Seaborn (df.boxplot(), sns.boxplot() — tez, 5.7); bezash (title/label). Tuzoqlar: bimodal yashirinish (histogram kerak), kam ma'lumot (box plot ishonchsiz), outlier chegara (1.5 standart), tick_labels yo'q (qaysi quti). Amaliyot — boxplot, qismlar, guruh, outlier. Ixcham. Taqqoslash.

2.7. Box plot tuzoqlari

Box plot asosiy tuzoqlari: bimodal yashirinish (box plot shakl detal yo'q — bimodal (ikki cho'qqi) box plotda bir xil (median/kvartil — ikki cho'qqi ko'rinmaydi); histogram 5.5-bob shakl uchun; box plot + histogram); kam ma'lumot (kam nuqta — kvartil/median beqaror; box plot ishonchsiz; katta namuna); outlier chegara (1.5IQR — standart lekin qat'iy emas; kontekstga — ba'zan 3IQR; box plot standart 1.5); tick_labels yo'q (ko'p quti — qaysi guruh; tick_labels); median vs o'rtacha (box plot median (chiziq) — o'rtacha emas; qiyshiqda farqli 4.2); ustma-ust taqqoslash (box plot yonma-yon — yaxshi; lekin juda ko'p (50 quti) chalkash); taqsimot shakli (box plot — kvartil; shakl (normal? qiyshiq?) histogram/violin). Sabab: box plot shakl/ma'lumot nozik (bimodal yashirin, kam ma'lumot — jim xato). Yechim: histogram (shakl), katta namuna, tick_labels, median tushun. Tuzoqlar — bimodal, kam ma'lumot, outlier chegara, tick_labels.

2.8. Box plot — ixcham taqsimot va taqqoslash

Box plot asosiy g'oyasi — ixcham taqsimot va taqqoslash: taqsimotni beshtalik xulosa (4.4 — min/Q1/median/Q3/max) bilan ixcham ko'rsatadi (quti — kvartil/IQR; median — markaz; mo'ylov — diapazon; outlier — chet); guruh taqqoslashda tengsiz (ko'p quti yonma-yon — median/tarqoqlik/outlier bir qarashda). ax.boxplot (quti — 5 son), qismlar (quti Q1-Q3, median chiziq, mo'ylov 1.5*IQR, outlier), guruh taqqoslash (ko'p quti — tick_labels), outlier (avtomatik — IQR usuli 4.4). Box plot vs histogram: box plot (ixcham, taqqoslash, outlier — shakl detal yo'q, bimodal yashirin); histogram (detal shakl, bir taqsimot). Foydalanish: guruh taqqoslash (10 shahar — median/tarqoqlik), outlier (chet — tozalash 6-qism), ixcham taqsimot (5 son). Data Science'da keng (guruh taqqoslash — EDA 9-qism; outlier — tozalash). Bu 4.4 (kvartil, beshtalik xulosa) davomi (box plot — vizual) va 5.5 (histogram — shakl), 5.7 (seaborn — violin) bilan. Box plot — ixcham taqsimot va taqqoslash (beshtalik xulosa, guruh). Ixcham. Taqqoslash.

3. Tez ma'lumotnoma

import matplotlib.pyplot as plt

# BOX PLOT (beshtalik xulosa — 4.4):
fig, ax = plt.subplots()
ax.boxplot(data)

# QISMLAR:
#   quti — Q1 dan Q3 gacha (o'rta 50% — IQR)
#   median chiziq — 50% (markaz)
#   mo'ylov (whisker) — 1.5*IQR gacha (asosiy diapazon)
#   outlier — chetdagi nuqta (avtomatik)

# GURUH TAQQOSLASH (ko'p quti yonma-yon):
ax.boxplot([shahar1, shahar2, shahar3], tick_labels=["T", "S", "B"])

# BOX PLOT vs HISTOGRAM:
#   box plot — ixcham, taqqoslash, outlier (shakl detal YO'Q)
#   histogram — detal shakl (bimodal), bir taqsimot

# PANDAS/SEABORN (tez — 5.7):
df.boxplot(column="maosh", by="shahar")

QOIDA: guruh taqqoslash (box plot) · shakl (histogram) · outlier (1.5*IQR) · median

Box plot xulosasi

Box plot — ixcham taqsimot va taqqoslash (beshtalik xulosa)
Quti (Q1-Q3, IQR) · median chiziq · mo'ylov (1.5*IQR) · outlier
Guruh taqqoslash — ko'p quti yonma-yon (tengsiz)
vs histogram — ixcham/taqqoslash (box) vs detal shakl (hist)
Bimodal yashiradi (histogram kerak)

4. Batafsil misollar

Misollar real matplotlib/numpy bilan (Agg — grafik xususiyatlari matn bilan tekshiriladi) ishlaydi.

Misol 1 — Box plot

"""Box plot (real matplotlib/numpy)."""

import matplotlib
matplotlib.use("Agg")
import matplotlib.pyplot as plt
import numpy as np


def main() -> None:
    np.random.seed(0)
    data = np.random.normal(50, 15, 200)

    fig, ax = plt.subplots()
    bp = ax.boxplot(data)

    print("=== 1. Box plot ===")
    print(f"  qutilar: {len(bp['boxes'])}")

    print("\n=== 2. Median ===")
    median_chiziq = bp["medians"][0].get_ydata()
    print(f"  median: {round(median_chiziq[0], 0)}")

    print("\n=== 3. Beshtalik xulosa ===")
    print(f"  Q1: {round(np.percentile(data, 25), 0)}")
    print(f"  median: {round(np.percentile(data, 50), 0)}")
    print(f"  Q3: {round(np.percentile(data, 75), 0)}")

    print("\n=== 4. Tushuntirish ===")
    print("  box plot — beshtalik xulosa (ixcham)")
    plt.close(fig)
    print("  ⭐ Box plot — beshtalik xulosa 4.4-bob")


if __name__ == "__main__":
    main()

Natijaning muhim qismi:

=== 1. Box plot ===
  qutilar: 1

=== 2. Median ===
  median: 51.0

=== 3. Beshtalik xulosa ===
  Q1: 39.0
  median: 51.0
  Q3: 62.0

=== 4. Tushuntirish ===
  box plot — beshtalik xulosa (ixcham)
  ⭐ Box plot — beshtalik xulosa (4.4)

Nima ko'rsatdi: 2.1, 2.2-bo'limlar.

Misol 2 — Guruh taqqoslash

"""Guruh taqqoslash: box plot (real matplotlib/numpy)."""

import matplotlib
matplotlib.use("Agg")
import matplotlib.pyplot as plt
import numpy as np


def main() -> None:
    np.random.seed(0)
    shahar1 = np.random.normal(500, 100, 200)
    shahar2 = np.random.normal(400, 80, 200)
    shahar3 = np.random.normal(600, 150, 200)

    fig, ax = plt.subplots()
    bp = ax.boxplot([shahar1, shahar2, shahar3], tick_labels=["T", "S", "B"])

    print("=== 1. Uch quti ===")
    print(f"  qutilar: {len(bp['boxes'])}")

    print("\n=== 2. Medianlar ===")
    medianlar = [round(m.get_ydata()[0], 0) for m in bp["medians"]]
    print(f"  median (T, S, B): {medianlar}")

    print("\n=== 3. Eng yuqori median (B) ===")
    print(f"  eng yuqori: {['T','S','B'][medianlar.index(max(medianlar))]}")

    print("\n=== 4. Taqqoslash ===")
    print("  har shahar bir quti (median/tarqoqlik bir qarashda)")
    plt.close(fig)
    print("  ⭐ Guruh taqqoslash — ko'p quti yonma-yon")


if __name__ == "__main__":
    main()

Natijaning muhim qismi:

=== 1. Uch quti ===
  qutilar: 3

=== 2. Medianlar ===
  median (T, S, B): [np.float64(505.0), np.float64(388.0), np.float64(589.0)]

=== 3. Eng yuqori median (B) ===
  eng yuqori: B

=== 4. Taqqoslash ===
  har shahar bir quti (median/tarqoqlik bir qarashda)
  ⭐ Guruh taqqoslash — ko'p quti yonma-yon

Nima ko'rsatdi: 2.3-bo'lim.

Misol 3 — Outlier ko'rsatish

"""Outlier: box plot (real matplotlib/numpy)."""

import matplotlib
matplotlib.use("Agg")
import matplotlib.pyplot as plt
import numpy as np


def main() -> None:
    np.random.seed(0)
    data = np.random.normal(50, 10, 100)
    data = np.append(data, [120, 130, 5])   # outlierlar

    fig, ax = plt.subplots()
    bp = ax.boxplot(data)

    print("=== 1. Outlierlar (fliers) ===")
    outlierlar = bp["fliers"][0].get_ydata()
    print(f"  outlier soni: {len(outlierlar)}")

    print("\n=== 2. Outlier qiymatlar ===")
    print(f"  outlierlar: {sorted([int(v) for v in outlierlar])}")

    print("\n=== 3. IQR chegarasi 4.4-bob ===")
    Q1, Q3 = np.percentile(data, 25), np.percentile(data, 75)
    IQR = Q3 - Q1
    print(f"  yuqori chegara: {round(Q3 + 1.5*IQR, 0)}")

    print("\n=== 4. Tushuntirish ===")
    print("  box plot outlierni avtomatik (1.5*IQR — 4.4)")
    plt.close(fig)
    print("  ⭐ Outlier — chetdagi nuqta (avtomatik)")


if __name__ == "__main__":
    main()

Natijaning muhim qismi:

=== 1. Outlierlar (fliers) ===
  outlier soni: 3

=== 2. Outlier qiymatlar ===
  outlierlar: [5, 120, 130]

=== 3. IQR chegarasi 4.4-bob ===
  yuqori chegara: 79.0

=== 4. Tushuntirish ===
  box plot outlierni avtomatik (1.5*IQR — 4.4)
  ⭐ Outlier — chetdagi nuqta (avtomatik)

Nima ko'rsatdi: 2.5-bo'lim.

Misol 4 — Box plot vs histogram (bimodal)

"""Box plot vs histogram: bimodal (real matplotlib/numpy)."""

import matplotlib
matplotlib.use("Agg")
import matplotlib.pyplot as plt
import numpy as np


def main() -> None:
    np.random.seed(0)
    bimodal = np.concatenate([np.random.normal(30, 5, 500), np.random.normal(70, 5, 500)])

    print("=== 1. Bimodal ma'lumot ===")
    print(f"  ikki guruh: 30 va 70 atrofida")

    print("\n=== 2. Box plot (bimodal yashiradi) ===")
    fig, ax = plt.subplots()
    bp = ax.boxplot(bimodal)
    median = bp["medians"][0].get_ydata()[0]
    print(f"  median: {round(median, 0)} (~50 — ikki cho'qqi ko'rinmaydi)")
    plt.close(fig)

    print("\n=== 3. Histogram (bimodal ko'rsatadi) ===")
    fig, ax = plt.subplots()
    n, _, _ = ax.hist(bimodal, bins=20)
    print(f"  ikki cho'qqi: chap {int(n[:10].max())}, o'ng {int(n[10:].max())}")
    plt.close(fig)

    print("\n=== 4. Xulosa ===")
    print("  box plot ixcham (bimodal yashiradi), histogram shakl")
    print("  ⭐ Box plot vs histogram — ixcham vs detal shakl")


if __name__ == "__main__":
    main()

Natijaning muhim qismi:

=== 1. Bimodal ma'lumot ===
  ikki guruh: 30 va 70 atrofida

=== 2. Box plot (bimodal yashiradi) ===
  median: 49.0 (~50 — ikki cho'qqi ko'rinmaydi)

=== 3. Histogram (bimodal ko'rsatadi) ===
  ikki cho'qqi: chap 132, o'ng 142

=== 4. Xulosa ===
  box plot ixcham (bimodal yashiradi), histogram shakl
  ⭐ Box plot vs histogram — ixcham vs detal shakl

Nima ko'rsatdi: 2.4-bo'lim.

5. To'g'ri va noto'g'ri tushunishlar

6. Keng tarqalgan xatolar va yechimlari

1. Bimodal yashirinishi

ax.boxplot(bimodal)   # ikki cho'qqi ko'rinmaydi              # ⚠️
ax.hist(bimodal)   # shakl (histogram — 5.5)                  # ✅

2. Kam ma'lumot

ax.boxplot([1, 2, 3])   # beqaror (kvartil)                   # ⚠️
# katta namuna (ishonchli)                                    # ✅

3. tick_labels yo'q

ax.boxplot([a, b, c])   # qaysi quti qaysi                    # ⚠️
ax.boxplot([a, b, c], tick_labels=["A", "B", "C"])            # ✅

4. Median vs o'rtacha

# box plot chiziq — o'rtacha deb                              # ⚠️
# median (50% — qiyshiqda farqli 4.2)                         # ✅

5. Juda ko'p quti

ax.boxplot([50 guruh])   # chalkash                           # ⚠️
# kam guruh yoki saralab (top N)                              # ✅

6. Shakl uchun box plot

ax.boxplot(data)   # shakl (normal? qiyshiq?)                 # ⚠️
ax.hist(data)   # histogram (shakl — 5.5)                      # ✅

7. Outlier chegara

# 1.5*IQR qat'iy deb                                          # ⚠️
# whis= (kontekst — ba'zan 3*IQR)                              # ✅

7. Integratsiya — bu bilim qayerda kerak bo'ladi

• 4.4-dars (o'tilgan): Kvartil, beshtalik xulosa, IQR
• 5.5-dars (o'tilgan): Histogram (shakl)
• 5.7-dars: Seaborn (boxplot, violin)
• 6-qism: Tozalash (outlier — IQR)
• 9-qism (reja): EDA (guruh taqqoslash)

8. Eng yaxshi amaliyotlar

1. ax.boxplot — beshtalik xulosa 4.4-bob.

2. Guruh taqqoslash — ko'p quti (kuchli).

3. Shakl — histogram (box plot bimodal yashiradi).

4. tick_labels — qaysi quti.

5. Outlier — avtomatik (1.5*IQR).

6. Median (chiziq — o'rtacha emas).

7. Katta namuna (kvartil barqaror).

8. Box plot — ixcham taqsimot va taqqoslash.

9. Amaliy topshiriq

Vazifa 1: Bashorat qiling

1.  # box plot nima?
2.  # quti nima?
3.  # chiziq nima?
4.  # mo'ylov nima?
5.  # outlier qanday?
6.  # guruh taqqoslash?
7.  # box plot vs histogram?
8.  # bimodal ko'rinadimi?
9.  # kam ma'lumot?
10. # tick_labels?
11. # chiziq o'rtachami?
12. # nega box plot muhim?

Vazifa 2: Xatolarni tuzating

1.  ax.boxplot(bimodal)   # ikki cho'qqi

2.  ax.boxplot([1, 2, 3])   # kam

3.  ax.boxplot([a, b, c])   # qaysi quti

4.  # box plot chiziq = o'rtacha

5.  ax.boxplot(data)   # shakl

1.  ax.hist(bimodal) (shakl)

2.  katta namuna

3.  tick_labels=["A", "B", "C"]

4.  median (o'rtacha emas)

5.  ax.hist(data) (histogram)

Vazifa 3: Box plot

Modellang:

1. Beshtalik
2. Quti
3. Median
4. Ixcham

Vazifa 4: Qismlar

Modellang:

1. Quti (Q1-Q3)
2. Median
3. Mo'ylov
4. Outlier

Vazifa 5: Taqqoslash

Modellang:

1. Ko'p quti
2. Yonma-yon
3. tick_labels
4. Bir qarashda

Vazifa 6: vs histogram

Modellang:

1. Ixcham
2. Detal shakl
3. Taqqoslash
4. Bimodal

Vazifa 7: O'ylash

Box plot taqsimotni 5 son bilan ixcham ko'rsatadi va guruhlarni taqqoslashda tengsiz, lekin bimodal (ikki cho'qqili) taqsimotni yashiradi (histogram uni ochadi). Nima uchun box plot va histogram bir-birini to'ldiradi (biri ixcham/taqqoslash, biri detal shakl), va nega "har grafik turining o'z kuchi va kamchiligi bor" degan tushuncha muhim?

Nimani mustahkamlaydi: 2.4, 2.7-bo'limlar.

Xulosa

Bu darsda box plotni o'rgandik.

Eng muhim uch fikr:

1. Box plot va qismlar. Box plot (ax.boxplot(data)) — taqsimotni beshtalik xulosa 4.4-bob bilan ixcham ko'rsatadi. Qismlar: quti (Q1 dan Q3 — o'rta 50%, IQR), median chiziq (quti ichida — 50%, markaz; o'rtacha emas), mo'ylov (whisker — 1.5*IQR gacha, asosiy diapazon), outlier (mo'ylovdan tashqari — chetdagi nuqta, avtomatik).

2. Taqqoslash va outlier. Guruh taqqoslash — ko'p quti yonma-yon (ax.boxplot([a, b, c], tick_labels=[...]); 10 shahar — median/tarqoqlik/outlier bir qarashda; box plot tengsiz taqqoslashda). Outlier — avtomatik (1.5*IQR — 4.4; chetdagi nuqta; guruh outlier). Box plot outlier aniqlash uchun ideal (IQR usuli).

3. Ixcham vs detal. Box plot vs histogram — box plot (ixcham, guruh taqqoslash, outlier — shakl detal yo'q, bimodal yashiradi); histogram (detal shakl — bimodal ko'rinadi, bir taqsimot; taqqoslash qiyin). To'ldiradi (biri ixcham/taqqoslash, biri detal — birga to'liq; har grafik kuchi/kamchiligi — maqsadga tanlov). Box plot — ixcham taqsimot va taqqoslash (beshtalik xulosa, guruh). Data Science'da keng (guruh taqqoslash — EDA 9-qism; outlier — tozalash 6-qism). Bu 4.4 (kvartil) davomi (vizual) va 5.5 (histogram), 5.7 (seaborn — violin) bilan. Tuzoqlar: bimodal yashirinish (histogram), kam ma'lumot (beqaror), tick_labels, median vs o'rtacha.

Keyingi darsda Seabornni o'rganamiz: Matplotlib ustida qurilgan yuqori darajali kutubxona — chiroyli grafiklar, statistik vizualizatsiya (regplot, violinplot) kam kod bilan.