Statistics Class 10 Notes — Mean, Median, Mode Simple Hindi Me, NCERT Chapter 14

Statistics Class 10 Notes: Data Ka Matlab Samajhna

Statistics class 10 notes un students ke liye hai jinhe data dekh kar ghabrahat hoti hai. Board exam me jab lambi frequency table samne aati hai to kai students ye soch kar ruk jate hain ki ye sawaal to hoga hi nahi. Lekin sach ye hai ki Sankhyiki (Statistics) Class 10 ka sabse scoring chapter hai — formula yaad ho aur steps saaf hon to poore number milte hain. Is chapter me teen cheezein seekhni hain: mean (maadhya), median (madhyika) aur mode (bahulak). Teenon ka kaam ek hi hai — poore data ka ek representative number nikalna, bas tareeka alag hai.

Ye notes NCERT Class 10 Maths ke Chapter 14 (Statistics) par aadharit hain. Har formula ke saath ek solved example diya gaya hai, taaki formula sirf ratna na pade, samajh bhi aaye.

Statistics Class 10 Notes: Teen Basic Baatein

Pehle teen shabdon ka matlab seedhe shabdon me samajh lijiye:

• Mean (Maadhya): sabhi observations ka ausat. Sab ko jod kar ginati se bhaag dijiye.
• Median (Madhyika): data ko chhote se bade kram me rakhne par beech wala number. Aadhe observations isse neeche aur aadhe upar hote hain.
• Mode (Bahulak): wo number jo data me sabse zyada baar aata hai.

In teenon ko “central tendency” ke measures kehte hain — matlab ye batate hain ki data ka kendra kahan hai.

Mean (Maadhya): Ungrouped Data

Ungrouped data ka mean nikalna sabse aasan hai. Formula ye hai: Mean = (sabhi observations ka yog) / (observations ki sankhya).

Example: numbers 2, 4, 6, 8, 10 ka mean nikaliye. Yog = 2 + 4 + 6 + 8 + 10 = 30. Sankhya = 5. Isliye mean = 30 / 5 = 6. Isi data ka median bhi 6 hai, kyunki beech wala number 6 hai. Lekin mode is data me koi nahi hai, kyunki koi number dobara aaya hi nahi. Board exam me kabhi-kabhi ye trick poochhi jati hai — har data ka mode hona zaroori nahi hai.

Grouped Data Ka Mean: Step By Step

Board exam me zyada tar sawaal grouped data se aate hain. Class intervals aur frequencies di hoti hain. Steps ye hain:

1. Har class ka class mark (midpoint) nikaliye: class mark = (lower limit + upper limit) / 2.
2. Har class mark ko uski frequency se guna kijiye (f into x).
3. Sabhi f into x ka yog kijiye aur total frequency se bhaag dijiye.

Example: classes 0-10, 10-20, 20-30, 30-40, 40-50 hain aur frequencies 5, 8, 12, 10, 5 hain. Class marks honge 5, 15, 25, 35, 45. Ab f into x hoga: 5 into 5 = 25, 8 into 15 = 120, 12 into 25 = 300, 10 into 35 = 350, 5 into 45 = 225. Inka yog = 25 + 120 + 300 + 350 + 225 = 1020. Total frequency = 5 + 8 + 12 + 10 + 5 = 40. Isliye mean = 1020 / 40 = 25.5. Is example ko hum median aur mode ke liye bhi istemal karenge, taaki teenon ka farq saaf dikhe.

Median (Madhyika): Grouped Data

Median nikalne ke steps:

1. Cumulative frequency (cf) banayein — har frequency ko usse pehle ki frequencies me jodte jayein.
2. N = total frequency nikaliye. N/2 nikaliye.
3. Jis class ki cumulative frequency N/2 se pehli baar barabar ya zyada ho, wahi median class hai.
4. Formula lagayein: Median = l + ((N/2 – cf) / f) into h. Yahan l = median class ki lower limit, cf = median class se pehle wali class tak ki cumulative frequency, f = median class ki frequency, h = class ka size.

Upar wale example me: frequencies 5, 8, 12, 10, 5 hain, isliye cumulative frequencies hongi 5, 13, 25, 35, 40. N = 40, isliye N/2 = 20. Pehli baar 20 se zyada cumulative frequency 25 wali class me milti hai, yani 20-30 class hi median class hai. Yahan l = 20, cf = 13, f = 12, h = 10. Median = 20 + ((20 – 13) / 12) into 10 = 20 + (7/12) into 10 = 20 + 5.83 = 25.83 (lagbhag). Dhyaan dijiye: median class ko pehchanne me hi sabse zyada galti hoti hai — cumulative frequency dekh kar hi class chuniye, sirf frequency dekh kar nahi.

Mode (Bahulak): Grouped Data

Mode ke liye modal class chahiye — wo class jiski frequency sabse zyada ho. Formula ye hai: Mode = l + ((f1 – f0) / (2f1 – f0 – f2)) into h. Yahan l = modal class ki lower limit, f1 = modal class ki frequency, f0 = modal class se pehle wali class ki frequency, f2 = modal class ke baad wali class ki frequency, h = class ka size.

Usi example me sabse zyada frequency 12 hai, jo 20-30 class ki hai. Isliye modal class 20-30 hai. Yahan l = 20, f1 = 12, f0 = 8, f2 = 10, h = 10. Mode = 20 + ((12 – 8) / (24 – 8 – 10)) into 10 = 20 + (4/6) into 10 = 20 + 6.67 = 26.67 (lagbhag).

Ab teenon ko ek saath dekhiye: mean = 25.5, median = 25.83, mode = 26.67. Teenon paas-paas hain, kyunki data lagbhag symmetric hai. Jab data ek taraf jhuka hota hai to teenon me farq badh jata hai — isliye kaun sa measure kab istemal karna hai, ye samajhna zaroori hai.

Mean, Median, Mode Me Kaun Kab

• Mean tab accha hai jab data me koi bahut bada ya bahut chhota outlier na ho, kyunki mean har number se prabhavit hota hai.
• Median tab behtar hai jab data me kuch bahut bade ya bahut chhote numbers hon, kyunki median sirf beech ki position dekhta hai.
• Mode tab kaam aata hai jab ye jaanna ho ki sabse zyada baar kya aaya hai — jaise sabse zyada bikne wala shoe size ya sabse common marks.

Ek empirical relation bhi hai jo board exam me kabhi-kabhi poochha jata hai: Mode = 3 into Median – 2 into Mean. Ye relation lagbhag sahi hota hai, bilkul exact nahi. Hamare example me 3 into 25.83 – 2 into 25.5 = 77.5 – 51 = 26.5, jo asli mode 26.67 ke kaafi kareeb hai. Is relation ka istemal sirf tab kijiye jab teen me se do diye hon aur teesra nikalna ho.

Board Exam Ke Liye Tips

• Formula likhne me step mat chhodiye — board me steps ke number milte hain, sirf final answer ke nahi.
• Cumulative frequency ki column banane me galti mat kijiye; median ka sawaal aksar isi column ki galti se bigadta hai.
• Class mark nikalte waqt lower aur upper limit ka ausat lijiye, kisi ek limit ko class mark mat maan lijiye.
• Answer ko “lagbhag” (approximately) ke saath do decimal tak likhna theek hai, lekin steps poore dikhayein.
• Practice ke liye ye sawaal khud solve kijiye: classes 10-20, 20-30, 30-40, 40-50, 50-60 ki frequencies 4, 6, 10, 7, 3 hon to mean kitna hoga? Class marks 15, 25, 35, 45, 55 honge, f into x ka yog = 60 + 150 + 350 + 315 + 165 = 1040, total frequency = 30, isliye mean = 1040 / 30 = 34.67 (lagbhag). Agar aapka answer ye aaya to aapka method sahi hai.

Yaad Rakhne Wale Formula

• Ungrouped mean = observations ka yog / observations ki sankhya.
• Grouped mean = (f into x ka yog) / (frequencies ka yog).
• Median = l + ((N/2 – cf) / f) into h.
• Mode = l + ((f1 – f0) / (2f1 – f0 – f2)) into h.
• Empirical relation: Mode = 3 Median – 2 Mean (lagbhag).

In notes ko ek baar padh kar dobara apne haath se example solve kijiye — Sankhyiki haath se solve karne par hi pakki hoti hai, sirf padhne se nahi.

Statistics class 10 notes se judi aage ki jaankari ke liye Students category dekhein.

Statistics class 10 notes ko antim baar revise karte waqt mean, median aur mode ke formula ek saath likh kar dekh lijiye, kyunki statistics class 10 notes ki yahi chhoti si aadat board exam me kaam aati hai. Is aadat se statistics class 10 notes ka revision jaldi aur pakka ho jata hai.