Essays of Benjamin Franklin

An Introduction to the theory of statistics

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Monograph

Identifikator:: 1752429486

URN:: urn:nbn:de:zbw-retromon-127700

Document type:: Monograph

Author:: Franklin, Benjamin http://d-nb.info/gnd/118534912

Title:: Essays of Benjamin Franklin

Place of publication:: New York

Publisher:: G. P. Putnam's Sons

Year of publication:: 1927

Scope:: xi, 273 Seiten

Digitisation:: 2021

Collection:: Economics Books

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Document type:: Monograph

Structure type:: Chapter

Title:: IV. The examination of Dr. Benjamin Franklin in the british house of commons

Collection:: Economics Books

THEORY OF STATISTICS. EXERCISES. 1. (For this and similar estimates cf. ‘Report by Miss Collet on the Statistics of Employment of Women and Girls ” [C.—7564] 1894). If, in the urban district of Bury, 817 per thousand of the women between 20 and 25 years of age were returned as ‘‘ occupied ” at the census of 1891, and 263 per thousand as married or widowed, what is the lowest proportion per thousand of the married or widowed that must have been occupied ? 2. If, in a series of houses actually invaded by small-pox, 70 per cent. of the inhabitants are attacked and 85 per cent. have been vaccinated, what is the lowest percentage of the vaccinated that must have been attacked ? 3. Given that 50 per cent. of the inmates of a workhouse are men, 60 per cent, are ‘‘ aged ” (over 60), 80 per cent. non-able-bodied, 85 per cent. aged men, 45 per cent. non-able-bodied men, and 42 per cent. non-able-bodied and aged, find the greatest and least possible proportions of non-able-bodied aged men. 4. (Material from ref. 5 of Chap. I.) The following are the proportions per 10,000 of boys observed, with certain classes of defects amongst a number of school-children. 4 =development defects, B=nerve signs, D=mental dulness. N =10,000 (DY =739 (4)= 877 (4B)=338 (B)= 1,086 (BD)=455 Show that some dull boys do not exhibit development defects, and state how many at least do not do so. 5. The following are the corresponding figures for girls : — N =10,000 (D) =689 (4)= 682 (4B)=248 (B)= "850 (BD) =3863 Show that some defectively developed girls are not dull, and state how many at least must be so. 6. Take the syllogism “ All 4’s are B, all B’s are C, therefore all 4’s are C,” express the premisses in terms of the notation of the preceding chapters, and deduce the conclusion by the use of the general conditions of consistence. 7. Do the same for the syllogism ‘‘ All 4’s are B, no B’s are C, therefore no 4’s are C.” 8. Given that (4)=(B)=(C)=%4, and that (4B)/N=(4C)/N=p, find what must be the greatest or least values of p in order that we may infer that (BC)/N exceeds any given value, say g. 9. Show that if ry & © 4) _ = 2 52 Fi 2% Nr 3z (4B)_(4C)_(BO)_ : ENE Ey the value of neither « nor 7 can exceed %. 24 nd

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