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Frequency table se mean aur median

Short mein jawab

Frequency table mein har value ke saath likha hota hai ki wo kitni baar aati hai. Mean ke liye har value ko uski frequency se guna karein, guna-phal jodein aur kul frequency se bhaag dein. Median ke liye frequencies ek-ek karke jodein jab tak running total beech ke sthaan tak na pahunche; wahaan ki value median hai.

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Median aur uska badalna

Data ko kram mein lagaane par beech wali value median hai, jiske neeche aur upar barabar values hoti hain; values sam sankhya mein hon to ye beech ki do values ka ausat hai. Value jodne par kya hota hai? 4, 6, 8, 11, 13 lijiye, median 8. Median se badi 12 jodiye: ab chhah values hain aur median (8 + 11) ÷ 2 = 9.5 hai, yaani badh gaya. Uski jagah median se chhoti 2 jodiye to wo (6 + 8) ÷ 2 = 7 ho jaata hai. Median se badi value use sirf badha sakti hai ya waisa hi chhod sakti hai; chhoti value sirf ghata sakti hai ya waisa hi chhod sakti hai.

Median se badi, chhoti ya barabar value jodne par median kaise badalta hai
Median kaise badalta hai

Frequency table kya hai

Jab koi value bahut baar dohraaye, to har value likhna dheema hai. Frequency table har value ek baar uski frequency ke saath likhti hai, yaani wo kitni baar aati hai. Chapter ki class parivaar ke size likhti hai: 3 vidyaarthiyon ke parivaar mein 3 log, 11 ke 4, 9 ke 5, 7 ke 6, 3 ke 7, aur ek-ek vidyaarthi ke 8, 9 aur 10, kul 36 vidyaarthi.

Mean nikaalna

Ek lalchaata shortcut hai (3 + 4 + 5 + 6 + 7 + 8 + 9 + 10) ÷ 8 = 6.5, par ye har parivaar size ko ek hi baar ginta hai. Mean mein har value judni chahiye, isliye har size ko uski frequency se guna kiya jaata hai: 3 × 3 + 4 × 11 + 5 × 9 + 6 × 7 + 7 × 3 + 8 × 1 + 9 × 1 + 10 × 1 = 188. 36 vidyaarthiyon se bhaag dene par parivaar ka ausat size 188 ÷ 36 ≈ 5.22 milta hai.

Parivaar ke size ki frequency table se mean aur median, guna-phal aur running total ke saath
Frequency table se mean aur median

Running total se median

36 values mein median kram mein 18vi aur 19vi value ka ausat hai. Saare 36 number likhne ki jagah frequencies ka running total rakhiye: size 3 aur 4 sthaan 1 se 14 tak (3 + 11) bharte hain, aur size 5 sthaan 15 se 23 tak (14 + 9). Isliye 18vi aur 19vi dono values 5 hain, aur parivaar ka median size 5 hai.

Ek aur table: dart

Ek dart pratiyogita mein 62 vidyaarthiyon ne bull’s eye par lagaane ke liye 1 se 10 baar phenka: 1 ne 1 baar, 1 ne 4, 4 ne 5, 9 ne 6, 12 ne 7, 15 ne 8, 10 ne 9 aur 10 ne 10 baar. Nyuntam 1 hai aur adhiktam 10. Kul phenk 473 hain, isliye mean 473 ÷ 62 ≈ 7.63 hai. Median 31vi aur 32vi value ka ausat hai: running total 7 phenk par 27 aur 8 par 42 tak pahunchta hai, isliye dono 8 hain aur median 8 hai.

Dot plot bhi aise hi chalta hai

Dot plot ek frequency table hi hai jo dheriyon mein bani hai. Chapter ke plot mein, jo dikhaata hai ki 42 vidyaarthiyon ne hafte mein kitni baar cycle chalaayi, dheriyon ki oonchaai frequency hai: 3 ne 0 baar, 1 ne ek baar, 4 ne do baar, 7 ne teen baar, 7 ne chaar baar, 5 ne paanch baar, 4 ne chhah baar, 6 ne saat baar, 3 ne aath baar aur 2 ne das baar. Yaani kul 193 rides, mean lagbhag 4.6, aur median 4.

Hafte mein cycle ki rides: mean aur median ke saath dot plot
Hafte mein cycle ki rides

Mean ya median?

Dono kendra batate hain, par alag tarah se. Mean har value ka istemaal karta hai aur unki dooriyaan santulit karta hai, isliye ek bahut badi ya bahut chhoti value use door kheench sakti hai. Median sirf kram par nirbhar hai, isliye tab tak nahi hilta jab tak values beech ko paar na karein. Dono ko, nyuntam aur adhiktam ke saath, dekhne se data ki poori tasveer milti hai.

Aur padhein: mean (ausat) kya hai?, line graph kaise padhein?, chapter ke notes aur NCERT solutions.

Practice karo

  1. 36 values mein median kin sthaanon ki values ka ausat hai?

    1. (a) 17 aur 18
    2. (b) 18 aur 19
    3. (c) 1 aur 36
    4. (d) sirf 18
    Jawab dekho

    Jawab: (b) 18 aur 19

  2. 62 vidyaarthiyon ne bull’s eye ke liye 1 se 10 baar dart phenke (Exercise 11 ki table). Median kitni baar hai?

    1. (a) 6
    2. (b) 7
    3. (c) 8
    4. (d) 9
    Jawab dekho

    Jawab: (c) 8

  3. Median se chhoti value jodne par median ho sakta hai:

    1. (a) sirf bada
    2. (b) chhota ya waisa hi
    3. (c) hamesha waisa hi
    4. (d) do guna
    Jawab dekho

    Jawab: (b) chhota ya waisa hi

  4. Value 2 teen baar aur value 5 do baar aaye to mean nikaaliye.

    Jawab dekho

    Jawab: (2 × 3 + 5 × 2) ÷ (3 + 2) = (6 + 10) ÷ 5 = 16 ÷ 5 = 3.2.

  5. 42 vidyaarthiyon ke cycling dot plot mein median 4 kyon hai?

    Jawab dekho

    Jawab: 42 values mein median 21vi aur 22vi value ka ausat hai. Running total 3 rides par 15 aur 4 rides par 22 tak pahunchta hai, isliye ye dono values 4 hain.

Students ke sawal

Frequency table se mean kaise nikaalte hain?

Har value ko uski frequency se guna kijiye, sab guna-phal jodkar data ka jod nikaaliye, aur frequencies ke jod, yaani values ki sankhya, se bhaag dijiye.

Frequency table se median kaise nikaalte hain?

Pehle beech ka sthaan nikaaliye: n values ke liye (n + 1) ÷ 2, ya n sam ho to uske dono taraf ke do sthaan. Phir sabse chhoti value se frequencies jodte jaaiye jab tak running total us sthaan tak na pahunche.

Value jodne se median kaise badalta hai?

Median se badi value use sirf badha sakti hai ya waisa hi chhod sakti hai; chhoti value sirf ghata sakti hai ya waisa hi chhod sakti hai. Jab beech ki values barabar hon, jaise kai values median ke barabar hon, to wo waisa hi rehta hai.

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