APPENDIX III. ANSWERS TO PROBLEMS; MISCELLANEOUS PROBLEMS. Answers to Problems. 7. $1,312, since salaries between 1,000 and 1,100 are to be reckoned as averaging 1,050, and similarly for the other groups. A. D., σ and P. E. A. D., σ and P. Median = 98.61. respectively .51, .68 and .41. E. from Av. =re A. D., σ and P. E. spectively 7.5, 9.6 and 6.4. Median = 40.2. from median = respectively 7.5, 9.6 and 6.4. = 18. The great frequency of measures 98.0, 99.0 and 98.6 is probably due to the tendency of the observer to record even numbers and the 'normal' temperature. The two cases reported 96.0 were very likely observed simply as between 96 and 97 and then by an error Av. 98.58. A. D. = .53. recorded as 96.0. = 75 50 per cent. of 50 per cent. of 19. Case I. The average is 155.6; the A. D. from it of the cases above it is 18; that of the cases below it is 15. the cases above it deviate less than 12.9 from it. the cases below it deviate less than 13.3 from it. per cent. of the cases above it deviate less than 25.2 from it. 75 per cent. of the cases below it deviate less than 22.1 from it. The mode is the 140-149 group. Using 145 as an approximate modal point, the A. D. from the mode of the cases above it is 20.8; that of those below it is 11.0. 50 per cent. of the cases above it deviate less than 17.0 from it. 50 per cent. of all the cases below it deviate less than 9.9 from it. per cent. of the cases above it deviate less than 29.6 from it. cent. of the cases below it deviate less than 17.1 from it. 75 75 per 19. Case II. The average is 5.24; the A. D. from it of the cases above it is 1.2; that of those below it is .5. 60 per cent. 53.5 per of the cases above deviate less than 1.0 from the average. cent. of the cases below deviate less than .5 from the average. The mode is 5.000; the A. D. from it of the cases above it is 1.43; that of those below it is .51. 61 per cent. of the cases above it deviate less than 1.25. 94.5 per cent. of the cases below it deviate less than .50. 20. The mode and median and P. E.'s from them and various percentile values. 21. If the form of distribution is a rectangle, If the form of distribution is that of the normal probability If A – B = B - C and BC= C-D, etc., A+ 2.8 A. D. or + 3.2, according to the correction made. 66 66 " " (2) + .08. In the answers to problems 30-42 the unreliabilities are given in terms of the P. E.true measure-obtained measure. These can be turned into t-o. and A. D.t.-o. by multiplying by 1.4826 and 1.1843 respectively. |