Time Series Analysis

''wemwgj­vwni ingvwbi iwng'' knx` ¯§„wZ wWMÖx K‡jR dwKinvU , ev‡MinvU cwimsL¨vb(1g cÎ) Aa¨vq 10 Kvjxb mvwi we‡k­lb Time Series Analysis wek¦vm Cgvb Avjx ‡gvevt 01714-847436 cÖfvlK (cwimsL¨vb) knx` ¯§„wZ wWMÖx gnvwe`¨vjq cix¶K gva¨wgK I D”P gva¨wgK wk¶v‡evW©, h‡kvi

cÖkœ t 1 Kvjxb mvwi wK ? Gi Dcv`vbmg~n Av‡jvPbv Ki|

    A_ev, Kvjxb mvwi ej‡Z wK eyS ? GKwU Kvjxbmvwii wewfbœ Dcv`vb¸‡jv eb©bv Ki|

DËi tÑ Kvjxb mvwitÑ mg‡qi mv‡_ cwieZ©bkxj †Kvb Pj‡Ki wbw`©ó mgq Aš—i Aš—i cÖvß gvbmg~n‡K Zv‡`i NUvi mgq Abymv‡i wj‡L †h mvibx ev Z_¨mvwi cvIqv hvq Zv‡K Kvjxb mvwi e‡j|

       D`vnib¯^iƒc wewfbœ erm‡i evsjv‡`‡ki †jvKmsL¨v †gvU Drcv`b, Avq-e¨q, Avg`vwb-ißvwb BZ¨vw`|

Kvjxb mvwii Dcv`vb tÑ Kvjxb mvwii Pj‡Ki gvbmg~n wewfbœ Kvib Øviv cÖfvweZ n‡q _v‡K, hv‡`i‡K Kvjxbmvwii Dcv`vb ejv nq| GB Dcv`vb ¸‡jv‡K cÖavbZ: Pvifv‡M fvM Kiv nq|

wb‡b¥ Kvjxb mvwii Dcv`vb¸‡jv Av‡jvPbv Kiv njtÑ

1.      `xN©Kvjxb cÖebZv ev mvavib aviv tÑ mg‡qi m‡½ A‡bK Pj‡Ki gv‡bi e„w× , n«vm ev w¯’wZkxjZvi cÖebZv j¶¨Kiv hvq| †hgbÑ evsjv‡`‡ki †jvKmsL¨v cÖwZeQi e„w× cv‡”Q| A_©vr Bnvi cÖebZv DaŸ©gyLx| wKš‘ evsjv‡`‡ki †jvKmsL¨v e„w×i nvi, g„Zy¨i nvi cÖwZeQi K‡g hv‡”Q| Bnv‡`i cÖebZv wbb¥gyLx| Avevi MZ K‡qK eQi hveZ evsjv‡`‡ki †mvbvi `vg †gvUvgywU w¯’i| |A_©vr evsjv‡`‡ki †mvbvi `v‡gi w¯’wZkxjZvi cÖebZv j¶¨ Kiv hvq| Kvjxb mvwi Dcv‡Ëi Giƒc e„w×, n«vm ev w¯’wZkxjZvi cÖebZv‡K `xN©Kvjxb cÖebZv ev mvavib aviv e‡j| Bnv‡K Τ Øviv cÖKvk Kiv nq|

2.      FZzMZ †f` tÑ FZz cwieZ©‡bi mv‡_ mv‡_ Kvjxbmvwii g‡a¨ †h cwieZ©b †`Lv hvq Zv‡K FZzMZ †f` e‡j| Bnv‡K Ѕ Øviv cÖKvk Kiv nq|G ai‡bi cwieZ©‡bi ch©vq  Kvj mvavibZ : GK ermi| wKš‘ G cwieZ©‡bi ch©vq mvßvwnK, gvwmK, ˆÎgvwmK ev lbœvwmK I n‡Z cv‡i| GQvov G ai‡bi cwieZ©b GK ermi mgqKv‡ji g‡a¨ †h‡Kvb mgq GK ev GKvwaK evi NU‡Z cv‡i Ges †Kvb †Kvb †¶‡Î cÖwZermi GKB mgq ev Gmg‡qi KvQvKvwQ n‡Z cv‡i| FZzMZ †f` cÖavbZ : `yB Kvi‡b n‡q _v‡K| h_vÑ 

1)    Rjevqy I AvenvIqvi Kvi‡b 

2)    mvgvwRK AvPvi ev ixwZbxwZ|

         D`vnib¯^iƒc ejv hvq, el©vKv‡j QvZv I ivev‡ii RyZvi g~j¨ e„w× cvq| kxZKv‡j ckgx Kvc‡oi g~j¨ e„w× cvq Ges kvK-mwâi g~j¨ n«vm cvq| Avevi Mi‡gi w`‡b ˆe`y¨wZK cvLv, †iwd«Rv‡iUi , kxZZvc wbqš¿b hš¿ BZ¨vw`i g~j¨ kxZKvj A‡c¶v †ewk _v‡K| G cwieZ©b¸‡jv Rjevhy I AvenvIqvi Kvi‡bB n‡q _v‡K|

        C` ev c~Rvi mgq wewfbœ wRwb‡mi Pvwn`v e„w× cvq e‡j `vg I e„w× cvq| gvN-dvêyb gv‡m weevn Abyôvb †ewk nq e‡j H mgq D³ Abyôv‡b e¨eüZ wRwbm c‡Îi Pvwn`v Ges `vg e„w× cvq| G RvZxq cwieZ©b mvgvwRK AvPvi ev ixwZ bxwZi Kvi‡b N‡U _v‡K|

3       Pµ-µwgK n«vm-e„w× tÑ †Kvb †Kvb Kvjxb mvwii Pj‡Ki gvb ch©vq µ‡g n«vm-e„w× N‡U Ges cwieZ©‡bi GBaviv `xN©-mgq e¨vcx cwijw¶Z nq| Kvjxb mvwii †h Dcv`vb `xN©mgq e¨vcx ch©vqµ‡g A_P AwbqwgZ weiwZ‡Z n«vm-e„w× N‡U Zv‡K Pµ-µwgK n«vm-e„w× e‡j| Bnv‡K C Øviv cÖKvk Kiv nq|

       Gi ch©qKvj mvavibZ : GK erm‡ii AwaK nq| e¨emv-evwbR¨ I K…wl‡¶‡Î A_©vr A_©‰bwZK Kg©Kv‡Û Pµ-µwgK n«vm-e„w× cwijw¶Z nq| G PµKv‡ji wbw`©ó †Kvb mxgv †bB| mvavibZ : 3 ermi n‡Z 8/10 erm‡ii g‡a¨ GKwU PµKvj n‡Z cv‡i| G PµKvj wewfbœ †`‡ki Rb¨I wewfbœ iKg n‡Z cv‡i|

4.     AwbqwgZ †f` tÑ AvKw¯§K †Kvb Kvib Øviv Kvjxb mvwii cwieZ©b mvwaZ n‡j Zv‡K AwbqwgZ †f` e‡j| Gi †Kvb wbw`©ó ch©vq ev mgqKvj †bB| Pj‡Ki gv‡bi cwieZ©b GLv‡b nVvr K‡i N‡U _v‡K| †hgbÑ fywgK¤úb, eb¨v, So, ag©NU, ivR‰bwZK cU cwieZ©b, hy×-weMÖn cÖf„wZ Avgw¯§K Kvi‡b A_©‰bwZK Ges e¨emv-evwb‡R¨ nVvr cwieZ©b j¶¨ Kiv hvq| D‡j­wLZ kw³¸‡jvi Kvi‡b Kvjxb mvwii AvKw¯§K cwieZ©b nq e‡j G cwieZ©b‡K AwbqwgZ †f` ejv nq| Bnv‡K I Øviv cÖKvk Kiv nq|

cÖkœ tÑ 2 Kvjxb mvwii Dcv`vb mg~‡ni ga¨Kvi m¤úK©wU †jL|

A_ev, Kvjxb mvwii †hvMwewa I ¸bb wewa e¨vL¨v Ki|

A_ev, Kvjxb mvwii ( MvwbwZK) g‡Wj/ cÖwZK…wZ mg~n Av‡jvPbv Ki|

DËi tÑ Kvjxb mvwii Dcv`vbmg~‡ni g‡a¨ m¤úK© tÑ Kvjxbmvwi we‡k­l‡b Kvjxb mvwii wewfbœ Dcv`v‡bi g‡a¨ GKwU m¤úK© we`¨gvb _v‡K| m¤úK©¸‡jv mvavibZ : `yB cÖKvi| h_vÑ

1)      †hvRbkxj m¤úK© ev †hvM wewa

2)      ¸bbkxj m¤úK© ev ¸bb wewa|

‡hvRbkxj m¤úK© tÑ †Kvb †Kvb cwimsL¨vbwe` g‡b K‡ib †h, Kvjxbmvwii †h‡Kvb gvb Gi PviwU Dcv`v‡bi cÖfve-mg~‡ni †hvMd‡ji mgvb| A_©vr hw` †Kvb Kvjxb mvwii  mg‡qi gvb nq, Zvn‡j †hvRbkxj m¤úK© Abyhvqx Kvjxbmvwii Dcv`vb¸‡jvi m¤úK© njÑ

           †hLv‡b,  mvavib aviv ev `xN©Kvjxb cÖebZv|

                    FZzMZ †f`|

                    Pµ-µwgK n«vm-e„w×|

                    AwbqwgZ †f`|

¸bbkxj m¤úK© tÑ †Kvb †Kvb cwimsL¨vbwe` g‡bK‡ib †h, Kvjxb mvwii †h †Kvb gvb Gi PviwU Dcv`v‡bi cÖfve mg~‡ni ¸bd‡ji mgvb| A_©vr hw`  †Kvb Kvjxbmvwii  mg‡qi gvb nq, Zvn‡j ¸bbbkxj m¤úK© Abyhvqx Kvjxbmvwii Dcv`vb¸‡jvi m¤úK© njÑ

cÖkœ t 3 Kvjxb mvwii eûj cÖwZK…wZ †KvbwU ?

DËi tÑ e¨emv-evwbR¨ I A_©‰bwZK †¶‡Î Kvjxb mvwii Dcv`vb ¸‡jvi g‡a¨ Mybbkxj m¤úK© a‡i we‡k­lb Kiv nq| ZvB Kvjxb mvwii Dcv`vb¸‡jvi ¸bbkxj g‡Wj ev cÖwZK„wZB eûjfv‡e e¨eüZ nq|

cÖkœ tÑ 4 mvavib aviv ej‡Z wK eyS ?

DËi tÑ mvavib aviv/ `xN©Kvjxb cÖebZv tÑ `xN©mgq a‡i msM„nxZ Kvjxb mvwi‡Z Z_¨gvb mg~‡ni  µgn«vm ev µge„w× ev w¯’wZkxj Ae¯’vi cÖebZv j¶¨ Kiv hvq| Kvjxb mvwi‡Z Pj‡Ki GB `xN© †gqvw` mvavib n«vm ev e„w× ev w¯’wZkxjZvi cÖebZv ev ˆewkô¨‡K `xN©Kvjxb cÖebZv ev mvavib aviv ejv nq|

cÖkœ tÑ 5 Kvjxb mvwii mvavib aviv ev `xN©Kvjxb cÖebZv wbb©‡qi wewfbœ c×wZ¸‡jv eb©bv Ki|

DËi tÑ mvavib aviv/ `xN©Kvjxb cÖebZv mvavibZ t PviwU c×wZ‡Z cwigvc Kiv hvq| h_vÑ

1. gy³ n¯— ev ‰jwLK c×wZ
2. AvavMo c×wZ
3. Pjgvb ev MwZkxj ev Pwjòz Mo c×wZ
4. b~b¨Zg evM© c×wZ|

gy³n¯— ev ‰jwLK c×wZ tÑ GB c×wZ‡Z cÖ_‡g MÖvd ev QK KvM‡R Kvjxb mvwii Z_¨vejxi mgq‡K  A‡¶ we›`y AvKv‡i ¯’vcb Kiv nq| AZ:ci we›`y¸‡jv †K Aej¤^b K‡i gy³ n‡¯— GKwU eµ ev mij‡iLv AsKb Kiv nq| GB †iLvi MwZB Kvjxb mvwii `xN©Kvjxb cÖebZv ev mvavib aviv wb‡`©k K‡i|

AavMo c×wZ tÑ GB c×wZ‡Z cÖ_gZ Kvjxb mvwii Z_¨ewj mgvb `yfv‡M fvM Kiv nq| we‡Rvo msL¨K Z_¨gvb _vK‡j ga¨gvbwU ev` w`‡q mgvb `yfv‡M fvM Ki‡Z nq| `yfvM Kivi ci cÖ‡Z¨K fv‡Mi Z_¨gv‡bi Mo wbb©q  Kiv nq| AZ:ci cÖ‡Z¨K As‡ki mg‡qi ga¨we›`y eivei Mo we›`yØq QK KvM‡R ¯’vcb Kiv nq| GLb GB we›`y `ywU ms‡hvM K‡i †h †iLv cvIqv hvq ZvB Kvjxb mvwii cÖebZv wb‡`©k K‡i|

        cÖ‡qvRb †ev‡a cÖebZv †iLvwU Dfq w`‡K ewa©Z K‡i Kvjxbmvwii c~‡e©i †Kvb gvb wbiƒcb Kiv hvq| A_ev fwelr†Zi †Kvb gv‡bi c~e©vfvm †`Iqv hvq|

myweav tÑ

1. GB c×wZ mnR‡eva¨ Ges AwZmn‡R AsKb Kiv hvq|
2. GB c×wZ‡Z Kvjxb mvwii Rb¨ AswKZ †iLv e¨w³i wfbœZvq GKB _v‡K|
3. Kvjxb mvwii Z_¨ mij ˆiLK n‡j GB c×wZ‡Z wbf©i‡hvM¨ cwigvc cvIqv hvq|

Amyweav tÑ

1. Kvjxb mvwii Z_¨ mij ‰iwLK bv n‡j GB c×wZ‡Z mvavib avivi mwVK cwigvc m¤¢e bq|
2. GB c×wZ‡Z MvwbwZK Mo e¨envi Kiv nq, d‡j cÖvß djvdj cÖvš—xq gvb Øviv cÖfvweZ nq|
3. GB c×wZ‡Z cÖvß djvd‡ji Dci Pµ-µwgK n«vm e„w×i cÖfve _vKvi m¤¢vebv _v‡K|

Pjgvb ev MwZkxj ev Pwjòz Mo c×wZ tÑ GB  c×wZ‡Z KZ eQi ev mg‡qi Rb¨ Giƒc Mo wbb©q Kiv n‡e Zv wba©vib Ki‡Z nq| awi, 5 eQi e¨vcx Pjgvb Mo wbb©q Ki‡Z n‡e| G‡¶‡Î Kvjxb mvwii Z_¨vejx n‡Z 1g 5wU gvb †hvM K‡i 5 w`‡q fvM K‡i †h Mogvb cvIqv hvq Zv ga¨eZ©x mgq A_©vr 3q eQi eivei ¯’vcb Kiv nq| GLb 1g Z_¨gvb ev` w`‡q cieZ©x 5wU Z_¨gvb A_©r 2q gvb n‡Z 6ô gvb ch©š— †hvM K‡i 5 w`‡q fvM K‡i 2q Mo gvb PZz_© eQi eivei wjL‡Z nq| Giƒc ch©qµ‡g Dc‡ii w`K n‡Z GK GKwU gvb ev` w`‡q cieZ©x 5wU gvb‡i Mo wbb©q Ki‡Z n‡e †h ch©š— Z_¨gvb †kl bv nq|

        Abyiƒcfv‡e, 2,3,4,.......... BZ¨w` eQi wfwËK Pjgvb Mo wbb©‡qi Rb¨ D‡j­wLZ c×wZ Aej¤^b Kiv hvq|

         wKš‘ †Rvo msL¨v wfwËK eQj n‡j ga¨¯’vb eivei †Kvb eQi _v‡Kbv| †hgbÑ 4eQi wfwËK Pjgvb Mo wbb©q Ki‡j ga¨eZ©x †Kvb eQi cvIqv hvq bv| ZvB 1g cÖvß Mo 2q I 3q eQ‡ii gvSvgvwS emv‡Z n‡e| Gfv‡e 2q Mo, 3q I 4_© eQ‡ii gvSvgvwS emv‡Z n‡e| Gfv‡e cieZ©x meMo‡KB `ywU eQ‡ii gvSvgvwS emv‡Z n‡e| Gfv‡e cÖvß Mo¸‡jv †h‡nZz †Kvb PQj eivei Ae¯’vb K‡ibv| ZvB cÖ_‡g cÖvß Mo gvb¸‡jvi `ywU `ywU K‡i Avevi Pjgvb Mo wbb©q Ki‡Z nq| 2q `dv Mo wbb©q K‡i M‡oi 1g gvb †K 3q eQi eivei, 2q gvb‡K 4_© eQi eivei, 3q gvb‡K 5g eQi eivei Ges Gfv‡e me Mo‡K eQi ¸‡jvi wecix‡Z emv‡Z n‡e|

         Gfv‡e cÖvß Pjgvb Mo ¸‡jv Zv‡`i mgq eivei QK KvM‡R ¯’vcb K‡i †h we›`y¸‡jv cvIqv hvq Zv †iLv Øviv mshy³ K‡i cÖ‡qvRbxq cÖebZv †iLv cvIqv hvq|

myweav tÑ

1. GB c×wZwU AwaKZi mnR‡eva¨ Ges MvwbwZK RwUjZv †bB|
2. GB c×wZ‡Z AwZwi³ Z‡_¨i ms‡hvRb Kiv n‡j Mbbv Kv‡h©i †Zgb †Kvb Amyweav nqbv|
3. GB c×wZ‡Z mgq Kvj mwVK n‡j Pµ-µwgK n«vm-e„w× I FZzMZ †f` m¤ú~b© `~i n‡q hvq|

Amyweav tÑ

1. GB c×wZ‡Z Kvjxb mvwii cÖ`Ë mKj eQ‡ii Rb¨ Pjgvb Mo wbb©q Kiv hvq bv|
2. Kvjxb mvwii Z_¨vejx‡Z mij ˆiwLK m¤úK© bv _vK‡j GB c×wZ SuzwK c~b©|
3. GB c×wZi mgqKvj wba©vib Kiv A‡c¶vK„Z RwUj|
4. GB c×wZ cwieZ©bkxjZvi †Kvb m~Î †g‡b P‡jbv, d‡j Bnv Øviv Kvjxb mvwi m¤ú‡K© c~e©vfvm †`Iqv hvq bv|

b~b¨Zg eM© c×wZ tÑ b~b¨Zg eM©c×wZ‡Z †Kvb Z_¨mvwii ch©‡ew¶Z gvb I cÖZ¨vwkZ gv‡bi wePy¨wZi e‡M©i mgwó b~b¨Zg ch©v‡q _v‡K|Kvjxb mvwi‡K QK KvM‡R Dc¯’vc‡bi ci cÖvß †iLvi cÖK…wZ we‡ePbv K‡i b~¨bZg eM©c×wZ‡Z `xN©Kvjxb cÖebZv ev mvavib aviv wbb©q Kiv nq|

awi, `xN©Kvjxb MwZ‡iLv GKwU mij †iLv hvi mgxKib nj,

‡hLv‡b,  n‡jv ¯^vaxb PjK,  n‡jv, Aaxb PjK Ges  I  n‡jv `ywU aª“eK|

GLb, †h‡Kvb mgq  Gi Rb¨ ch©‡ew¶Z gvb  n‡j  Ges  Gi g‡a¨ wePz¨wZ n‡e|

      

    

    

GLb,  I  Gi gvb Ggb fv‡e wbiƒcb Ki‡Z n‡e †hb,  Gigvb b~¨bZg eM©c×wZ e¨envi K‡i Avgiv cvB|

 Ges

cÖ`Ë Kvwjb mvwii Z_¨ e¨envi K‡i  Ges  Gi gvb wbb©q K‡i  bs mgxKi‡b emv‡j `xN©Kvjxb MwZi mgxKib cvIqv hv‡e| cÖvß mgxKi‡b cÖwZwU  Gi gvb ewm‡q GKwU K‡i  Gi gvb cvIqv hv‡e Ges GB gvb¸‡jv QK KvM‡R ¯’vcb Ki‡j `xN©Kvjxb MwZ‡iLv ev mvavib aviv †iLv cvIqv hv‡e|

       Mbbvi myweav‡_© mg‡qi ga¨we›`y‡K g~j K‡i Avgiv cvB,  ; myZivs  Ges  wbb©‡qi m~Î n‡e,  Ges

myweav tÑ

1.      GB c×wZ‡Z Kvjxb mvwi‡Z cÖ`Ë mKj mg‡qi Rb¨ mvavib avivi gvb wbb©q Kiv m¤¢e|

2.      MvwbwZK wfwË _vKvi Kvi‡b c×wZwU eûj cÖPwjZ|

3.      cÖvß mvavib avivi mgxKib e¨envi K‡i fwel¨Z cÖebZv m¤ú‡K© wbf©i‡hvM¨ c~e©vfvm †`Iqv hvq|

Amyweav tÑ

1.      Ab¨vb¨ c×wZ A‡c¶ Mbbv Kvh© A‡c¶vK…Z RwUj|

2.      GB c×wZ‡Z AwZwi³ Z‡_¨i ms‡hvRb ev we‡qvRb Kiv n‡j Avevi bZzb K‡i Mbbv Kvh© m¤úbœ Ki‡Z nq|

3.      GB c×wZ‡Z c~e©vfvm cÖ`v‡bi †¶‡Î Kvjxb mvwii Ab¨vb¨ Dcv`vb¸‡jvi cÖfve D‡c¶v Kiv nq|

cÖkœ tÑ 6 Kvjxb mvwii e¨envi ev ¸i“Z¡ Av‡jvPbv Ki|

DËi tÑ e¨emvwqK Kg©Kv‡Ûi cÖvq cÖwZwU ‡¶‡ÎB Kvjxb mvwi e¨envi Kiv nq| A_©bxwZ , e¨emv, ivóª cwiPvjbv, Ges cwiKíbv, weÁvb, †R¨wZwe©`¨v, mgvRweÁvb, Dw™¢`we`¨, M‡elbv Kvh© BZ¨vw` ‡¶‡Î Kvjxb mvwi Lye ¸i“Z¡c~b©|

wb‡¤§v³ †¶Îmg~‡n Kvjxbmvwii e¨vcK e¨envi j¶¨ Kiv hvq|

1. GKwU †`‡ki eZ©gvb Ae¯’v we‡k­lb K‡i fwel¨r RvZxq A_©‰bwZK cwiKíbv cÖbq‡b Bnvi e¨envi LyeB Zvrch©c~b©|
2. Kvjxb mvwi we‡k­lb cÖwµqv‡K mgvR weÁv‡bi †¶‡ÎI e¨envi Kiv hvq|
3. wkíKviLvbvi gvwjKMb Kvjxb mvwii we‡k­lb Øviv wk‡íi Drcv`b , weµq, Avq, Avg`vwb wKsev ißvbx BZ¨vw`‡Z KLb wK cwieZ©b n‡Z cv‡i †m m¤ú‡K© my®úó avibv jvf Ki‡Z cv‡i|
4. AZxZ Kg©KvÛ we‡k­lb K‡i fwel¨r Kg©cwiKíbv MÖn‡b Kvjxb mvwi e¨cKfv‡e e¨envi Kiv nq|
5. A_©bxwZ Ges e¨emvwqK Kg©Kv‡Ûi †h‡Kvb †¶‡Î AMÖMwZ Kvjxb mvwi we‡k­l‡bi gva¨‡g g~j¨vqb Kiv m¤¢e|
6. FZzMZ cwieZ©b I Pµ-µwgK n«vm-e„w× †R‡b Myi“Z¡c~b© wm×vš— MÖn‡b mnvqZv Ki‡Z Kvjxb mvwi e¨eüZ nq|
7. RvZxq ch©v‡q ivóªxq Kvh© cwiPvjbvq ¸i“Z¡c~b© cwiKíbv cÖbq‡b Kvjxb mvwi we‡k­l‡bi fywgKv Ab¯^xKvh©|

cÖkœ tÑ 7 Kvjxb mvwi we‡k­lb wK ? Kvjxb mvwi we‡k­lb Gi D‡Ïk¨ wjL|

DËitÑ Kvjxb mvwi we‡k­lb tÑ  Kvjxb mvwi we‡k­lb ej‡Z Dnvi Dcv`vb¸wji AbymÜvb , cwigvc I c„_KxKi‡bi gva¨‡g Z_¨gvb‡K Dnv‡`i cÖfvegy³ Kiv eySvq| Kvjxb mvwii Pj‡Ki gvb Dnvi PviwU Dcv`vb Øviv cÖfvweZ nq| GB Dcv`vb¸wj wbb©q I `~ixKib‡KB Kvjxbmvwi we‡k­lb e‡j|

Kvjxb mvwi we‡k­l‡bi D‡Ïk¨ tÑ

1. †h Kvib ev Dcv`v‡bi Øviv Kvjxb mvwii Z_¨gvb¸‡jv cÖfvweZ nq †m¸‡jv wPwýZK‡i Zv‡`i cÖfve cwigvc Kivi Rb¨ Kvjxb mvwi we‡k­lb Kiv nq|
2. Kvjxb mvwii Z_¨gv‡bi Ab¨vb¨ mewKQz wVK †i‡L H Kvib ev Dcv`vb¸‡jvi cÖfve G‡K G‡K Ab‡c¶fv‡e eR©b K‡i Dcv`vb¸‡jv m¤ú‡K© c~e©vfvm †`qvI Kvjxb mvwi we‡k­l‡bi Ab¨Zg D‡Ïk¨|

         GQvov A_©bxwZ, e¨emv-evwbR¨, cÖK…wZK ev mvgvwRK weÁv‡bi wewfbœ w`K e¨vL¨v Ki‡ZI Kvjxb mvwi we‡k­lb Kiv  nq|

 

‡mŠR‡b¨ t whwb cwimsL¨vb wel‡qi Ab¨Zg RbwcÖq Ges mK‡ji wbKU kª×vfvRb GKRb gvbyl Ges Avgvi cig wk¶K | hvi Fb †Kvb w`b fyjevi bq| 

                                                                                                                                                                                                      

            Zvi GK Rb AbyMZ QvÎ

†gv t gyiQvwjb mi`vi

          †gvevt 01925-425876

01718-365468

01918-365468

Central Tendency B.B.A 2nd

Central Tendency

1. Find out the mean from the following data:

     Age(year): 10,        28,        37,          45,           25,             36,           50.

2. Calculate Arithmetic mean from the following data:

     Daily Wages(in taka) : 50    60     80    90     120     150

      No of workers           :   5     7      12    15       8          3

3. Calculate Arithmetic Mean from the following data:

       Marks             : 0-10         10-30        30-60        60-100         100-120

 No of Students     :   5               12              25             8                    3

4. Find out the mean from the following data:

     Daily Wages(in taka) : 10-20      20-30       30-40     40-50       50-60

      No of workers           :     5             10            15           20            10

5. Calculate Arithmetic mean from the following frequency distribution :

H.W Marks    :  10-19             20-29            30-39             40-49           50-59       60-69

No of Students:    10                 17                  30                  51                 29              9

6. Calculate Arithmetic Mean from the following frequency distribution : H.W

       Monthly Salary(in tk)                                Number of Workers

500 but less than 600                                            4

600 but less than 700                                          10

 700 but less than 800                                         14

 800 but less than  900                                        12

  900 but less than  1000                                      4

1000 but less than  1100                                      2           

7. Honours Coaching Center wants to pay bonus  to the numbers of staffs. The bonus is to paid as follows

                Monthly Salary (in tk)                                 Bonus ( in tk)

               1000 and not exceeding 1200                              500

               1200 and not exceeding 1400                              600

1400 and not exceeding 1600                              700

1600 and not exceeding 1800                              800

1800 and not exceeding 2000                              900

      2000 and not exceeding 2200                             1000

      2200 and over                                                     1100

Actual salary of the numbers of staff is given unders :

1100,    2000,   1800,   1950,   2180,   1870,   1600,   1500,   1980,   1680,   1700,   1780,   1750,   1100,   1200,   1480,   1550,   2450,   1250,   1100,   1620,   1300,   1500,   1850.

Req:  1) What is the total bonus paid ?

         2) What is the average bonus paid ?

8.   A company limited wants to pay bonus to the members of staff . The bonus is to be paid as follows : H.W

                                     Monthly Salary (in tk)                                 Bonus ( in tk)

  300  and not exceeding 400                                                  100

               400 and not exceeding 500                                                   120                              

500 and not exceeding 600                                                   140                              

600 and not exceeding 700                                                   160                            

700 and not exceeding 800                                                    180                           

      800 and not exceeding 900                                                    200                             

      900 and not exceeding 1000                                                  220                        

                     1000 and not exceeding 1100                                                240

Actual Salary of the members of the staffs is given unders:

tk.  325,   378,   420,   620,   455,   620,   660,   680,   725,   863,   832,   942,   952,   800,   1002,   1025,   1100,   610,   625,   736,   382,   540,   463,   578,   723,   690,  

Req: 1) How much the company would need to pay by way of bonus ?

        2) What shall be the average bonus paid per workers ?

Combined Mean

9. There are two branches of a company employing 100 and 80 respectively . If Arithmetic   

    mean of the  monthly salaries paid by two branches are tk. 4570 and 6750 respectively.   

    Find out the A.M of the salaries of the employees of the company as a hole.

10. There are three sections in B.B.S Honours 3rd year in a certain college. The numbers of students in each sections and the average marks obtain by them in the paper of business statistics in the annual examination are as follows: H.W

Section                         Average Marks of B.S                           No of Students

A                                                     75                                                 50

B                                                     60                                                 60

C                                                     55                                                 55

Find out the average marks obtained by the students of three sections taken

11. The mean weight of 150 students in a certain class in 60kg. The mean weight of boys in the class is 70kg and the girls is 55kg. Find out the numbers of boys and the numbers of girls in the class. H.W

12. The mean marks in Statistics of 100 students of a class was 72. The mean of marks of boys 75,While there numbers was 70. Find out the mean marks of the girls in the class.

13. The mean of a combined groups of men and women is 30 years. If mean is of the groups of the men is 32 and that of women is 35. Find out the (%) of men and women in the groups.

14. The average monthly wages of all workers in a factory is tk. 444 . If the average wages is paid to male and female workers are tk. 480 and tk.360 respectively. Find out the percentage male and female workers by the company. H.W.

15. The average weekly wages for a groups of 25 persons working in a factory was calculated to be tk. 378.4. It was later discovered that one figure was misread as 160 instead the correct value is tk. 200. Calculated the correct average weight.

16. The mean marks of 420 students were found to be 70. Later on it was discovered that a score of 45 was misread as 34. Find the correct mean corresponding to correct mean. H.W.

17. The mean of 200 observations was 50. Latter on it was discovered that two observations were wrongly read as 92 and 80 instead of 192 and 88. Find out correct mean.

18. The mean salary paid to 10000 employees in a factory was to be tk. 2804. Latter on it was discovered that the wages of two employees was wrongly taken as 2970 and 3650 instead of 3650 and 4650. Find out  correct mean. H.W

Median

1. Calculate median from the following data.

29        54       57       33       70       61       86       72       88

2. Calculation median from the following data.

Marks                : 5      7        10        12        15        18        20

No of  Students : 6        4        8        1           7           3        4    

3. Calculation median from the following Frequency distributions :

Class Interval : 30-40      40-50     50-60     60-70     70-80

Frequency      :    2             6             18          10          8

4. Calculation median from the following frequency distributions:

Marks              : 20-29          30-39           40-49         50-59           60-69

No of Students :    16               31                50               20                8

5.  Calculation median from the following frequency distributions:

Class intervals      : 0-100        100-250         250-500        500-600        600-700

Frequency            :     5                  7                    30                15                   10

6. Calculation median from the following data . H.W

 290       544       576       331       704       617       864       722       880       550

7. Calculation median from the following data:

Marks               : 55        70        100        122        100        50        20

No of students : 4            6           8           12           7           3          2      

8. Calculation median from the following frequency distributions .H.W

Class Interval     : 10-20       20-30       30-40       40-50

Frequency          :      8              11            18             10

9. Calculation median from the following frequency distributions. H.W

Marks               : 10-29         30-49         50-59         70-89         90-109

No of Students :     16               31              50              20               8

10. Calculation median from the following Frequency distribution.

Class intervals : 0-10           10-25         25-50       50-60          60-70

Frequency       :    5                   7              30              15              10

11. 5% of the workers in a firm employing a total of 2000 workers earn less than tk.2.00 per hour, 480  

       earn form tk.2.00 to tk.2.24 per hour , 35% earn from tk.2.25 to tk.2.49 per hour. 370 earn from

       tk.2.50 to tk.2.74 per hour, 12% earn form tk.2.75 to tk.2.99 per  hour and rest earn tk.3.00 to tk.

       more per hour. What is the median of wages.

12. 10% of workers in a firm employing a total of 1000 workers earn less than tk.5.00 per day, 200 earn

       between tk.5.00 and tk.10 per hour, 30% earn form tk.10 and tk.15 , 250 earn between tk. 15 and

       tk.20 per hour and rest tk.20 and above. What is the median wages.

13. Calculation median from the following frequency distributions patterning to the profits tk(core) of 125

       companies:

Profits (tk core)                                            Numbers of  Companies

Less than 10                                                          4

Less than 20                                                         16

Less than 30                                                         40

Less than 40                                                         76

Less than 50                                                         96

Less than 60                                                        112

Less than 70                                                        120

Less than 80                                                        125

Geometric Mean

1.      Calculation Median from the following data.

29         54         57         33         70         61         86         72         88

2. Calculation median from the following data.

Marks                : 5                7                10                12                15                18                20

No of Students  :6                 4                8                   1                 7                   3                  4

2.      Calculation median from the following Frequency distribution:

Class Interval  : 30-40      40-50        50-60        60-70         70-80

Frequency       :      2            6                18             10               8

Harmonic Mean

1.      Calculation median from the following data :

                     290     544     576     331     704     617     864     722     880     550

2. Calculation Median from the following data :

 Marks             :  55     70     100     122     100     50     20    

No of students :  4        6         8       12        7        3       2

3        Calculation median from the following Frequency distribution.

Class interval : 10-20         20-30          30-40          40-50         50-60

Frequency      :     8                11                18               10              8

Quartiles , Deciles percentiles and Mode

1.Calculation quartiles ( 1^st & 3^rd ) from the following data :

29,       54,       57,       33,       70,       61,       86,       72,       88

2. Calculation Quartiles ( 1^st & 3^rd ) from the following  frequency distribution :

     Daily Wages ( in tk)  : 50,       60,       80,       90,       120,       150,      

     No of workers           :   5,         7,         12,       15,         8,          3

3.Find out the quartiles ( 1^st & 3^rd ) from the following data :

Daily Wages ( in tk) : 10-20        20-30        30-40        40-50        50-60        60-70

No of Workers          :     5               10              15             20             10             5 

4.Calculate Quartiles ( 1^st & 3^rd) From the following frequency distribution :

   Marks       :   10-19        20-29        30-39        40-49        50-59        60-69        70-79

   No of stu  :       10             17             30              51             29              9                5

5. Calculate D1,D3, & D5 from the following frequency distribution :

    29        20        54        88        61        91        72        86        70        39

6. Calculation Deciles ( D4, D7, & D9) from the following frequency distribution :

      Marks     :   55        70        100        122        100        50        20

     No of stu :    4          6            8            12           7          3        2

7. Calculation Deciles ( D1,D4, & D9) from the following frequency distribution :

    Class Interval   : 10-20        20-30        30-40        40-50        50-60

    Frequency        :     8              11               18              10             4

8. Calculate Deciles ( D1, D5 & D9) from the following frequency distribution :

    Marks       : 10-29        30-49        50-69        70-89        90-109

    No of stu  :     16              31             50             20               8

9. Calculation 2^nd Quartiles , D4 and D7 from the following frequency distribution :

   Marks       : 5        7        10        12        15        18        20

   No of stu  : 6        4          8        10          7          3         4

10. Calculation median, Quartiles and Deciles ( D4 & D6) from the following frequency distributions :

       Class intervals  :  0-10        10-25        25-50        50-60        60-70        70-100

       Frequency        : 5                   7               30              15              10               2

11. From the following data draw the ogive and determine the median, 1^st & 3^rd Quartiles  & 4^th deciles  

      from it. And verify the result by formula:

Class interval : 40-44           45-49           50-54           55-59           60-64           65-69

Frequency     :      3                  5                  7                  11                  9                  7

12. Calculation percentiles ( 40^th & 65^th ) from the following data :

29,       54,       57,       33,       70,       61,       86,       72,       88

13. Calculation 25^th and 69^th percentiles from the  following data :

Marks             : 55      70      100      122      100      50      20

No of student :   4       6           8         12        7         3       2

14. Find out the percentiles 60^th and 90^th from the following data :

Daily Wages( in tk.)  : 10-20      20-30      30-40      40-50      50-60      60-70

No of Workers          :      5           10             15         20             10             5      

15. Calculate percentiles 70^th and 10^th from the following frequency distribution :

Marks          :10-19             20-29             30-39             40-49             50-59             60-69             70-79

No of stu     :     10                  17                  30                  51                  29                  9                       5

16. The profits earned by 100 companies during 2005-2006 are given below :

Profits                  :    20-30       30-40      40-50      50-60      60-70      70-80      80-90

No of companies :       4                 8           18          30                15         10            8

17. A frequency distribution of the length of Telephone calls monitored at the switch board of an office is given bellow:

         Last of Calls ( in Min's)            No of Calls

0 and under  2                              10

2 and under  4                              25

4 and under  6                              20

6 and under  8                              40

            8 and under  10                              5

       1) Calculation the arithmetic mean of the calling time

      2) Determine and explain the meaning of 75% percentiles of the distribution.

18. From the following table showing the wages distribution on a certain  a factory :

   Weekly Wages ( in take)              No of companies

120-140                                  8 

140-160                                 12

160-180                                 20

180-200                                 30

200-220                                40

220-240                                32

240-260                                18

260-280                                   7

280-300                                   6

300-320                                   4

1) Determine the percentage of workers who earned between tk 175 and tk 225

2) The percentage of workers who earned more than tk 250 per week

3) The percentage of workers who earned less than tk 200 per week

19. The following  relates to the wages of 150 employees in  a certain companies :

Wages ( in take)                     No of Employees

20-25                                      7  

25-30                                     18

30-35                                    20

35-40                                    40

40-45                                    30

45-50                                    10

50-55                                    15

55-60                                    10

1) Calculation the wages limit for the middle 50% of the wages employees.

2) Calculation the wages limit for the middle 20% of the wages employees.

20. Calculation the mode from the following frequency distribution :

Marks      :    3            4            7            8            9            10

No of stu :    5            10         25          15          10            3    

21. Calculation mode from the following frequency distribution :

Marks       : 20-30             30-40            40-50            50-60            60-70            70-80

No of stu  :      7                  13                  20                  23                 25                 2

22. The following table gives the daily wages distribution of employees of a commercial organization

Daily Wages   :  250-300       300-350       350-400       400-450       450-500       500-550       550-600

No of emm     :          25                 30                55                   67                 39                14            10

1) Compute arithmetic mean and median of the distribution    2) Find the wages range of the 50%

employees    3) It is decided to collect tax from those having income of tk 530 ad avobe . What (%)

of the employees are taxable.

23. The weekly income distribution of  600 families are given below :

Weekly income ( in take)                      No of families

Below -300                                    69

300-600                                     167                       

600-900                                      206

900-1200                                   65

1200-1500                                 58

1500-1800                                 25

1800- avobe                              10

1)      Find out the limit of the weekly income of central 50% families .

2)      It is decides to collect tax from those families having income tk1400 and above. What (%) of the families are taxable

3)      Find out the mean , median and mode

4)      The percentages of families who earned less than tk375 and tk1225

5)      The percentages of families who earned above tk1200

Missing Frequency

1.      From the following data find out the missing frequency when mean is 30.76

Marks             : 20    24    28    32    36    40

No of student : 3       7      ?      20    8      5

2.      From the following data find out the missing frequency when mean is 28

Class Interval : 0-10     10-20     20-30     30-40     40-50     50-60

Frequency      :    12          18         27           ?            17           6

3.      From the following data find out the missing frequency when median is 46.

Marks :10-20         20-30         30-40         40-50         50-60         60-70         70-80         Total

No of stu : 12            30               ?                 65               ?                25              18            229

4.      From the following data find out the missing frequency when median is 35

Marks    : 0-10     10-20     20-30     30-40     40-50     50-60      60-70         Total

Students :   10            30        ?            40            ?           25           15             170

5.      The expenditure of 1000 families is given below :

Expenditure    :    40-59     60-79     80-99     100-119     120-139

No of families :    50             ?           500             ?             50

Find out the missing frequency. Mode of the frequency is 87.50.

6.      The Exp of 100 families is given below :

Exp   :          0-10     10-20     20-30     30-40     40-50          Total

No of fam  : 14             ?         26              ?           15              100

Find out the missing frequency. Mode of the frequency is 24.

7.      The expenditure of some families is given below :

Expenditure     :   0-10     10-20     20-30     30-40     40-50

No of families  :     14          ?             30          ?              6

Find out the missing frequency. Mode of the frequency is26  and  24.