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100 surnames were randomly picked up fro...

100 surnames were randomly picked up from a telephone directely and the distribution of the number of letters of the English alphabet in the surnames are obtained as follows

Determine the median and mean number of letters in the surnames .
Also, find the modal size of surnames

Text Solution

Verified by Experts

We have

Clearly , `A=11.5, h=3, Sigmaf_i=100 and Sigma(f_iu_i)=-106`
Mean , `barx=A+{hxx(Sigma(f_Iu_i))/(Sigmaf_i)}=11.5+{3xx((-106))/(100)}`
=11.5-3.18=8.32
Here N=100 `rArr N/2=50`
Cumulative frequency just greater than 50 is 76 and the corresponding class is 7-10 . Thus , the median class =36 `N/2=50`
`Median , M_e=l+{hxx((N/2-cf))/f}`
`=7+{3xx((50-36))/(40)}=7+(3xx(14)/(40))`
`7+(21)/(20)=7+1.05=8.05`
Mode =3(median)-2(mean)
`=3xx8.05-2xx8.32=24.15-16.64=7.51`
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