Question

Q.2 निम्न समंकमाला से मध्यका एवं बहुलक ज्ञात कीजिये :-
Calculate median and mode from following series -
0-10
10-20
20-30
30-40
40-50
प्राप्तांक (Marks)n
विद्यार्थीयों की संख्या
(No. of 3Student)
15
25
10
35
15​

Answer 1

Answer:

15.1 lexz voyksdu (Overview)

vkius iwoZorhZ d{kkvksa esa osQUnzh; izo`fÙk osQ ekiksa dk vè;;u fd;k gS tSls fd oxhZÑr ,oa

voxhZÑr vk¡dM+ksa dk ekè;] ekfè;dk ,oa cgqydA bu ekiksa osQ vfrfjDr gesa izk;% ,d nwljs izdkj

osQ eki dks Kkr djus dh vko';drk gksrh gS ftls izdh.kZu (iSQyko) dh eki dgk tkrk gSA ;g

ekè; vFkok ekfè;dk tSls eè;orhZ ekuksa ls izs{k.kksa dk fopj.k ekirk gSA

;g vè;k; ekè; fopyu] izlj.k] ekud fopyu tSlh egÙoiw.kZ izdh.kZu dh ekiksa dk

vè;;u djus vkSj vUr esa ckjackjrk caVuksa dk fo'ys"k.k djus ls lEcfUèkr gSA

15.1.1 izdh.kZu dh eki (Measure of Dispersion)

(a) ifjlj (Range): ifjlj ,slh izdh.kZu dh eki gS ftls cgqr gh ljyrk ls le>k ,oa Kkr

fd;k tkrk gS ifjlj bl izdkj ifjHkkf"kr gSA

ifjlj = lcls cM+k izs{k.k µ lcls NksVk izs{k.k

(b) ekè; fopyu (Mean Deviation)

(i) voxhZÑr vkadM+ksa dk ekè; fopyu

n izs{k.kksa x1

, x2

, ..., xn

, dk muosQ ekè; ( x ) osQ lkis{k] ekè; fopyu

M.D ( x ) =

| | i x x

n

−

(1)

mudh ekfè;dk osQ lkis{k ekè; fopyu Kkr djus osQ fy, fuEufyf[kr lw=k dk

mi;ksx fd;k tkrk gSA

M.D (M) =

| M| i x

n

−

(2)

(ii) vlrr ckjackjrk caVu dk ekè; fopyu (Mean Deviation for discrete

frequency distribution)

eku yhft, fn, gq, vkadM+ksa esa n lrr izs{k.k x1

, x2

, ... , xn gSa ftudh ckjackjrk,¡ Øe'k%