Frequency Table Se Mean Aur Median | Class 8 Maths Book 2 Ch 5

📘 Class 8 · Ganita Prakash Book 2Ch 5 · Tales by Dots and LinesPost 6 / 8⏱ 25–30 min

Frequency Table Se Mean Aur Median 📋

IS POST MEIN

Pehle Yeh Aata Hai?Kahani Concept Deep Concept Examples Real Life Galti 10 MCQs FAQs Practice HOTS Olympiad Recap

✅ Pehle Yeh Aata Hai?

Yeh post shuru karne se pehle, in teen sawaalon ko 1 minute mein khud try kijiye:

4 × 11 = ?
3 + 11 + 9 = ?
36 values ka median kaun si position(s)?

Answers dekho

44
23
18vi aur 19vi ka mean

Teeno sahi? Badhiya! Mean aur median yaad karo: Post 1.

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🎬 Kahani: Class Ke Parivaar

Teacher ne 36 bachchon se poochha: “Aapke ghar mein kitne log rehte hain?” Jawab board pe likhne mein poora board bhar jaata!

Priya ne ek chhoti si table banaayi: kitne parivaar mein 3 log, kitno mein 4… Isse kehte hain frequency table. 📋

“Ab bina 36 numbers likhe mean aur median kaise nikaalein?” Rohan ne poochha. Chalo seekhte hain!

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📖 Concept: Guna Karo, Jodo, Ginti Jodo

Step 1: Frequency table

Parivaar size (x)	3	4	5	6	7	8	9	10
Kitne bachche (f)	3	11	9	7	3	1	1	1

Kul f = 36. Frequency = koi value kitni baar aayi.

Step 2: Mean = Σ(x × f) ÷ Σf

x × f: 9, 44, 45, 42, 21, 8, 9, 10 → jod 188. Mean = 188 ÷ 36 ≈ 5.22.

WHY guna? 4 wale 11 parivaar = 4 + 4 + … (11 baar) = 44. Guna lambe jod ka shortcut hai.

Step 3: Cumulative frequency (ginti jodte jao)

x	3	4	5	6	7	8	9	10
Cumulative	3	14	23	30	33	34	35	36

Iska matlab: pehli 3 values “3” hain, 4th se 14th tak “4”, 15th se 23rd tak “5”…

Step 4: Median

36 values: median = 18vi aur 19vi ka mean. Dono 15 se 23 ke beech, yaani dono “5”. Median = 5.

WHY cumulative? Bina likhe pata chal jaata ki koi position kaun si value hai.

Step 5: Spreadsheet: computer pe yahi kaam

Spreadsheet mein columns A, B, C… aur rows 1, 2, 3… Har dabba (cell) ka naam column + row: jaise E5. Ek line ke cells: B3:G3; ek column: D2:D6.

=SUM(B3:G3) → B3 se G3 tak ka jod (ek bachche ke saare subjects ke marks).
=AVERAGE(B7:D7) → B7 se D7 ka mean.

WHY seekhein? 22 bachchon ke 6 subjects ke marks ka total aur average, haath se ghanton; spreadsheet mein second mein!

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🔐 Deep Concept: Mean Aur Median Alag Kyun?

Parivaar data mein mean 5.22, median 5. Thoda farak kyun? Kuch bade parivaar (8, 9, 10) mean ko upar kheenchte hain, median ko nahi.

Agar mean median se kaafi zyada ho, to samjho data mein kuch “bahut badi” values hain (ek lambi poonchh daayein taraf). Yeh data ka chupa hua aakaar batata hai! 🔐

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✏️ Solved Examples

Example 1 (Easy): Marks: 5 (2 bachche), 6 (3), 7 (5). Mean?

Σxf = 10 + 18 + 35 = 63, Σf = 10 → 6.3.

WHY sahi hai? 10 bachche, 63 ÷ 10 ✅

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Example 2 (Medium): Usi data ka median?

Cumulative: 2, 5, 10. 5vi aur 6thi values: 5vi = 6, 6thi = 7 → median 6.5.

WHY sahi hai? 5vi position “6” ke group ka aakhri ✅

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Example 3 (NCERT style): Parivaar data (36 bachche) ka mean aur median.

Mean = 188 ÷ 36 ≈ 5.22, median = 5.

WHY sahi hai? 18vi, 19vi dono “5” mein (15–23) ✅

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Priya ki trick: “Mean ke liye x × f, median ke liye cumulative!” 🎉

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🏠 Real Life Mein

🏫 School survey: bachchon ke ghar se doori, bhai-behen ki ginti.
🛒 Dukaan: kis size ke joote kitne bike.
🗳️ Census: parivaar ka size, umar ke groups.
💻 Spreadsheet: marks, kharcha, attendance ka hisaab.

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🧭 Kab Use Karein, Kab Nahi

Situation	Kya karein	Kyun
Values baar-baar aayein	✅ Frequency table	Chhoti, saaf
Mean	✅ Σxf ÷ Σf	Guna = lamba jod
Median	✅ Cumulative se position	Bina list ke
Mean = Σx ÷ Σf (f ka guna bhoole)	❌ Galat	Har value f baar

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❌→✅ Worked Mistake

Sawaal: x: 1, 2, 3 aur f: 5, 3, 2. Mean?

❌ Galat: “(1 + 2 + 3) ÷ 3 = 2.”

Galti kya hai? Frequencies bhool gaye ❌

✅ Sahi: (5 + 6 + 6) ÷ 10 = 1.7.

Yaad rakho: Har value utni baar gino jitni frequency.

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📝 10 MCQs

Q1. Frequency kya?

(a) Value kitni baar aayi

(b) Value ka size

(c) Mean

(d) Median

Solution dekho

Sahi jawab: (a)

(a) sahi: Sahi ✅
(b) galat: Nahi.
(c) galat: Nahi.
(d) galat: Nahi.

Q2. Parivaar data Σxf?

(a) 188

(b) 36

(c) 52

(d) 5.22

Solution dekho

Sahi jawab: (a)

(a) sahi: Sahi ✅
(b) galat: Σf.
(c) galat: Nahi.
(d) galat: Mean.

Q3. Mean?

(a) 5.22

(b) 5

(c) 6

(d) 4

Solution dekho

Sahi jawab: (a)

(a) sahi: 188 ÷ 36 ✅
(b) galat: Median.
(c) galat: Nahi.
(d) galat: Mode.

Q4. Median?

(a) 5

(b) 4

(c) 5.5

(d) 6

Solution dekho

Sahi jawab: (a)

(a) sahi: 18vi, 19vi = 5 ✅
(b) galat: Nahi.
(c) galat: Nahi.
(d) galat: Nahi.

Q5. Cumulative x = 5 tak?

(a) 23

(b) 9

(c) 14

(d) 30

Solution dekho

Sahi jawab: (a)

(a) sahi: 3 + 11 + 9 ✅
(b) galat: f hai.
(c) galat: x = 4 tak.
(d) galat: x = 6 tak.

Q6. Spreadsheet mein Farooq ke Maths marks E5 mein. E kya?

(a) Column

(b) Row

(c) Formula

(d) Sheet

Solution dekho

Sahi jawab: (a)

(a) sahi: Sahi ✅
(b) galat: 5 row hai.
(c) galat: Nahi.
(d) galat: Nahi.

Q7. =SUM(B3:G3) kya karta?

(a) B3 se G3 jod

(b) B3 × G3

(c) Average

(d) Sirf B3

Solution dekho

Sahi jawab: (a)

(a) sahi: Sahi ✅
(b) galat: Nahi.
(c) galat: AVERAGE se.
(d) galat: Nahi.

Q8. x: 1, 2, 3, f: 5, 3, 2 mean?

(a) 1.7

(b) 2

(c) 6

(d) 17

Solution dekho

Sahi jawab: (a)

(a) sahi: 17 ÷ 10 ✅
(b) galat: f bhoole.
(c) galat: Nahi.
(d) galat: Σxf.

Q9. 36 values ka median kaun si positions?

(a) 18, 19

(b) 18

(c) 36

(d) 1, 36

Solution dekho

Sahi jawab: (a)

(a) sahi: Sahi ✅
(b) galat: Even hai.
(c) galat: Nahi.
(d) galat: Nahi.

Q10. D2:D6 kitne cells?

(a) 5

(b) 4

(c) 6

(d) 2

Solution dekho

Sahi jawab: (a)

(a) sahi: D2, D3, D4, D5, D6 ✅
(b) galat: Nahi.
(c) galat: Nahi.
(d) galat: Nahi.

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❓ FAQs (Bachchon Ke Asli Sawaal)

1. Cumulative frequency kya?

Ab tak ki saari frequencies ka jod.

2. Odd total mein median?

(n + 1) ÷ 2 vi position.

3. Spreadsheet kaun se?

Koi bhi spreadsheet software (computer ya phone pe).

4. =AVERAGE aur =SUM ÷ ginti same?

Haan.

5. Mode kya?

Sabse zyada frequency wali value (yahan 4).

6. Bade data ke liye?

Frequency table ya spreadsheet sabse achha.

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🏋️ Practice Zone (12 Sawaal)

Q1. Easy x: 2, 4 f: 3, 1. Mean?

Solution dekho

10 ÷ 4 = 2.5.

Q2. Easy Usi ka median?

Solution dekho

2, 2, 2, 4 → 2.

Q3. Easy Parivaar data mein mode?

Solution dekho

Q4. Easy A1:A10 mein kitne cells?

Solution dekho

10.

Q5. Medium x: 10, 20, 30 f: 2, 5, 3. Mean?

Solution dekho

230 ÷ 10 = 23.

Q6. Medium Usi ka median?

Solution dekho

Cumulative 2, 7, 10 → 5vi, 6thi = 20 → 20.

Q7. Medium Shot (dart) data: trials 1 se 10, counts 1, 0, 0, 1, 4, 9, 12, 15, 10, 10. Kul students?

Data adapted from NCERT Ganita Prakash Part 2, Ch 5

Solution dekho

62.

Q8. NCERT style Usi data ka minimum aur maximum trials?

Solution dekho

1 aur 10.

Q9. NCERT style Usi ka mean?

Solution dekho

Σxf = 1 + 4 + 20 + 54 + 84 + 120 + 90 + 100 = 473 → 473 ÷ 62 ≈ 7.63.

Q10. NCERT style Usi ka median?

Solution dekho

31vi, 32vi: cumulative 1, 1, 1, 2, 6, 15, 27, 42 → dono “8” → 8.

Q11. Medium Formula ek bachche ke 6 subjects (B3 se G3) ka average?

Solution dekho

=AVERAGE(B3:G3).

Q12. Medium Frequency table ka fayda?

Solution dekho

Chhoti, saaf, hisaab aasaan.

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🧠 HOTS (Sochne Wale Sawaal)

Q1. Mean 5.22 aur median 5: data kis taraf jhuka?

Solution dekho

Daayein (bade parivaar kam par door).

Q2. Kya cumulative frequency kabhi ghat sakti?

Solution dekho

Nahi, sirf badhti ya same.

Q3. Ek nayi entry “10” jode: mean aur median?

Solution dekho

Mean badhega (10 > 5.22); median 37 values mein 19vi = 5, same.

Q4. Kya frequency table se original order pata chalta?

Solution dekho

Nahi, sirf kitni baar.

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🏆 Olympiad Corner

Q1. x: 1, 2, 3, 4 f: k, 2, 3, 4. Mean 3 ho to k?

Solution dekho

(k + 4 + 9 + 16) ÷ (k + 9) = 3 → k + 29 = 3k + 27 → k = 1.

Q2. x = 1 se 5, f = 2, 3, ?, 2, 1. Median 3 ho, to ? (x = 3 ki frequency) kitni ho sakti hai?

Solution dekho

? = 1: 9 values, 5vi = 2 ❌. ? = 2: 10 values, (2 + 3) ÷ 2 = 2.5 ❌. ? = 3: 11 values, 6thi = 3 ✅. To ? ≥ 3.

Q3. Spreadsheet: A1 = 5, A2 = 7, A3 = =A1+A2. A3?

Solution dekho

12.

Q4. =AVERAGE(A1:A3) (upar wala)?

Solution dekho

(5 + 7 + 12) ÷ 3 = 8.

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💗 CharuMam Motivation

Priya ne 36 numbers ko ek chhoti table mein samet diya. Smart tareeka, kam mehnat, sahi jawab! 📋

Badi cheez ko chhote, saaf hisson mein todna, padhaai ka bhi sabse achha tareeka hai. Aaj ka chapter 4 hisson mein, kal ka aasaan! 🌟

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🟢 Master Recap

Frequency table: value aur kitni baar.
Mean = Σ(x × f) ÷ Σf.
Median: cumulative frequency se position dhoondho.
Parivaar data: mean ≈ 5.22, median 5.
Spreadsheet: cell = column + row (E5); =SUM, =AVERAGE.

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👉 Aage Kya?

Ab data ko tasveer mein dekhenge: line graph se samay ke saath badlaav! 📈

← Pichla: Post 5 — Chhupi Value Dhoondho 📚 Chapter 5 ke saare posts Agla: Post 7 — Line Graph Padhna Aur Banana →

Koi doubt? CharuMam AI Tutor se poochho, ya comment mein likho! 💬

✅ Pehle Yeh Aata Hai?

🎬 Kahani: Class Ke Parivaar

📖 Concept: Guna Karo, Jodo, Ginti Jodo

Step 1: Frequency table

Step 2: Mean = Σ(x × f) ÷ Σf

Step 3: Cumulative frequency (ginti jodte jao)

Step 4: Median

Step 5: Spreadsheet: computer pe yahi kaam

🔐 Deep Concept: Mean Aur Median Alag Kyun?

✏️ Solved Examples

🏠 Real Life Mein

🧭 Kab Use Karein, Kab Nahi

❌→✅ Worked Mistake

📝 10 MCQs

❓ FAQs (Bachchon Ke Asli Sawaal)

🏋️ Practice Zone (12 Sawaal)

🧠 HOTS (Sochne Wale Sawaal)

🏆 Olympiad Corner

💗 CharuMam Motivation

🟢 Master Recap

👉 Aage Kya?

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