Lagnever AI English

Median aur outliers

Short mein jawab

Median sort kiye data ki beech waali value hai; ginti even ho to ye beech ki do values ka average hai. Outlier baaki data se bahut door ki value hai. Ye mean ko apni taraf kheench leta hai par median ko mushkil se hilaata hai, isliye outlier waale data ko aksar median mean se behtar dikhata hai.

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Jab average dhokha de

Yaangba ke parivaar ki lambaai 169, 173, 155, 165, 160 aur 164 cm hai, jiska mean 986 ÷ 6 ≈ 164.3 cm hai. Poovizhi ke parivaar ki lambaai 170, 173, 165, 118 aur 175 cm hai, jiska mean 801 ÷ 5 = 160.2 cm hai. Kya isse Yaangba ka parivaar lamba ho gaya? Asal mein nahi. Poovizhi ke parivaar ke paanch mein se chaar log 164.3 cm se lambe hain. Unka mean sirf isliye kam hai kyunki ek bachcha, 118 cm ka, baaki sab se bahut chhota aur kam umar ka hai. Yahan mean un paanch mein se chaar lambaaiyon se kam hai jinhe use dikhaana tha.

Median nikaalna

Sort ki hui lambaai: paanch values mein beech ki 170, aur chhe values mein 164 aur 165 ka average
Median nikaalna

Ek aur representative value hai median: data ko sort karo aur beech waala number lo. Poovizhi ka parivaar sort karne pe 118, 165, 170, 173, 175 hai, aur beech ka number 170 hai, isliye median lambaai 170 cm hai. Median ke neeche utni hi values hoti hain jitni upar. Yaangba ke parivaar mein chhe lambaaiyan hain, 155, 160, 164, 165, 169, 173, isliye beech mein koi akeli value nahi. Tab median beech ki do values ka average hota hai: (164 + 165) ÷ 2 = 164.5 cm. Yaangba ke parivaar mein mean aur median lagbhag barabar hain; Poovizhi ke parivaar mein kareeb 10 cm ka fark hai.

Outliers

Baaki data se bahut door ki value, jaise bachche ka 118 cm, outlier kehlaati hai. Ise hata do to Poovizhi ke parivaar ka mean 683 ÷ 4 = 170.75 cm aur median (170 + 173) ÷ 2 = 171.5 cm ho jaata hai. Mean 10 cm se zyaada uchhalta hai jabki median sirf 1.5 cm hilta hai. Outlier ne mean ko neeche kheench rakha tha; median pe uska asar lagbhag nahi tha.

Akhbaar ke panne, parivaar ki lambaai aur padhi kahaaniyon ke dot plots, mean aur median ke saath
Outlier mean ko kheenchta hai

Outlier upar ki taraf bhi ho sakta hai. Ek class ne bataaya ki chhuttiyon mein har student ne kitni chhoti kahaaniyan padhi: 6, 3, 0, 8, 2, 5, 15, 7, 12, 10, 40, 5, 0, 1 aur 8. Ek student ne 40 padhi. Mean 122 ÷ 15 ≈ 8.1 hai par median 6, isliye mean median se upar hai. 40 hata do to mean lagbhag 5.9 aur median 5.5 ho jaata hai. Ab ek akhbaar ke Monday se Sunday tak ke panne dekho: 16, 18, 20, 22, 26, 16 aur 10. Koi outlier nahi, isliye mean, lagbhag 18.3, aur median, 18, lagbhag barabar hain. To:

  • santulit data: mean ≈ median;
  • neeche ki taraf outlier: mean < median;
  • upar ki taraf outlier: mean > median.

Mean aur median central tendency ke maap kehlaate hain: ye wo value dikhate hain jiske aas paas data ikattha hota hai. Agar dono taraf outliers hon to wo ek doosre ko kuch had tak kaat dete hain, aur mean us outlier ki taraf khisakta hai jo zyaada door hai.

Data ke sire

Beech ki values poori kahaani nahi hain; minimum se maximum tak ka phailaav bhi maayne rakhta hai. Ek Grade 5 class mein ladkon ki lambaai 128 se 158 cm aur ladkiyon ki 136 se 156 cm hai, yaani sabse lamba aur sabse chhota dono students ladke hain. Phir bhi ladkon ka mean, 142.94 cm, ladkiyon ke mean, 146.9 cm, se kam hai. Average mein ladkiyan lambi hain, par isse har ladki har ladke se lambi nahi ho jaati. Dot plot, jisme number line ke upar har value ka ek dot hota hai, ye sab ek saath dikhata hai.

29 khajoor ke pedon ki lambaai ka dot plot, mean aur median ke saath
Khajoor ke pedon ki lambaai

Zero median run

Kya koi cricket team 407 run bana sakti hai jabki uske batsmen ka median score 0 ho? England ke gyaarah batsmen ne 19, 0, 0, 22, 158, 0, 184, 5, 0, 0 aur 0 run banaaye, aur 19 extras mile. Sort karne pe 11 scores mein chhatha score 0 hai, isliye median 0 hai. Par mean (407 − 19) ÷ 11 ≈ 35.27 run hai, kyunki do badi innings ne team ko sambhaala. Akela koi bhi number poori kahaani nahi batata; dono milkar, phailaav ke saath, batate hain.

Ye kyun zaroori hai

Reports aksar sirf average dete hain, aur ek outlier us average ko bhatka sakta hai. Median aur range poochhne se zyaada sachchi tasveer milti hai. Mean se tulna mean (average) kaise nikalein? mein karo, aur data ke graph data ko graph mein kaise dikhayein? mein dekho. Textbook ke sawaalon ke jawab Part 2 Chapter 5 ke NCERT solutions mein hain; poore Part 2 Chapter 5 ke notes dekho.

Practice karo

  1. 9, 2, 7, 4 aur 11 ka median kya hai?

    1. (a) 4
    2. (b) 7
    3. (c) 6.6
    4. (d) 9
    Jawab dekho

    Jawab: (b) 7

  2. 3, 8, 5, 10, 1 aur 6 ka median kya hai?

    1. (a) 5
    2. (b) 5.5
    3. (c) 6
    4. (d) 6.5
    Jawab dekho

    Jawab: (b) 5.5 Sort karne pe data 1, 3, 5, 6, 8, 10 hai. Beech ki do values 5 aur 6 hain, isliye median 5.5 hai.

  3. Data 0, 1, 2, 3, 5, 6 aur 40 mein 40 kya hai?

    1. (a) median
    2. (b) neeche ka outlier
    3. (c) upar ka outlier
    4. (d) mean
    Jawab dekho

    Jawab: (c) upar ka outlier

  4. Kisi data mein mean 8.1 aur median 6 hai. Outlier kahan hone ki sambhaavna hai?

    Jawab dekho

    Jawab: Upar ki taraf. Upar ka outlier mean ko median se upar utha deta hai, jaise bookworm data mein ek student ki padhi 40 kahaaniyon ne kiya.

  5. 16, 18, 20, 22, 26, 16 aur 10 ki range, mean aur median nikaalo.

    Jawab dekho

    Jawab: Sort karne pe: 10, 16, 16, 18, 20, 22, 26. Range 26 − 10 = 16 hai, mean 128 ÷ 7 ≈ 18.3 hai aur median 18 hai, chauthi value. Data santulit hai, isliye mean aur median paas hain.

Students ke sawal

Median kaise nikaalte hain?

Values ko chhote se bade kram mein sort karo. Values ki ginti odd ho to median beech waali value hai: 118, 165, 170, 173 aur 175 ka median 170 hai. Ginti even ho to beech ki do values ka average: 155, 160, 164, 165, 169 aur 173 ka median (164 + 165) ÷ 2 = 164.5 hai.

Outlier kya hota hai?

Aisi value jo baaki data se bahut alag ho, jaise aise parivaar mein 118 cm ka bachcha jiske baaki log 165 se 175 cm lambe hain, ya ek student jisne 40 kahaaniyan padhi jab zyaadatar ne 15 se kam padhi.

Median mean se kab behtar hai?

Jab data ke ek sire pe outlier ho. Outlier total ko, aur isliye mean ko, bahut badal deta hai, jabki beech ki value mushkil se hilti hai. Poovizhi ke parivaar ka mean, 160.2 cm, paanch mein se chaar lambaaiyon se kam hai, par median, 170 cm, parivaar ko theek dikhata hai.

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