Question

Groups 2-4 4-6 6-8 2-4 4-6 6-8 8-10 10-12 12-14 14-16 16-18 18-20 f f 102 18 40 24 47 80 21 15 66 Find a) Arithmetic mean b) Median c) Mode d) Differentiate between Arithmetic mean, Harmonic mean, and Geometric mean using 2 applications of each.

Answer 1

1. 
   solution Page No-01 Part @ frequeney distribution of gien data class -Mid value frequey cf fixi Intoval xi fi 18 18 54 2-4 4-6 120 5 24 42 6-8 7 47 89 | 329 8-10 9 80 1691720 = 102 1122 271 13 66 337 858 15 10-12 12-14 14-16 16-18 18-20 Total 40 21 17 3771 600 398 357 413 285 19 15 [{fl=413) |4*=4928 turi, N= efi'- 413 Efx=4445 Efixi ch A.M. = 4445 413 A.M. = 10.76 csscanned with CamScanner
   
   fage No-02 o zla 413 2 z = 206'5 so 5th class Median class with cf 271 Median of grouped data eth f where e lower limit of Median class h = class width f- frey of Medran clan C = Cumulative free of median class So, (413 –271) Med = 10+2 (413-2: 102 =10+2 (206:5-271) 102 Median a Part Mode=l+/Fi-fo 12 fi-fo-F2 Modal class= Max free class=5th class So, Mode=10+/102-80 whore l - lower limit of Modal class h = class width for free of preceding class f = freq of modal class F2 free of class sveceding to modal class +102-80 Borse)* 2 x 102-80-86 lot 44 50 Mode = 10.7586. CSScanned with CamScanner
   
   fage No-03 Part Anithmatic Mean! Har monks Mian It is calculated by It indicaty the dividing the sum of Central tendency by the numbers by the using the product number count. of their valu Q+b+.--+n axbxcx Grcomebric Man It is calculated bydriding the no of observations by the reciprocal of each no in the sones (axbxcx-n) n +++ sk Applications 0 It is often used in averaging things like rats. Simple calculations AM is widely used 6 It is widely in day to day used in statistiy with more uniform data ③ It is often used in Biology and medicines O canned with CamScanner 2 It is used in economics & statistic very often. The weighted VM is used in finance to ang multiples like price. earning ratio