Question

The objectives of a study by Skjelbo et al. were to examine (a) the relationship between Chloroguanide metabolism and efficacy in malaria prophylaxis and (b) the mephenytoin metabolism and its relationship to chloroguanide metabolism among Tanzanians. From information provided by urine specimens from the 216 subjects, the investigators computed the ratio of unchanged S-mephenytoin to R-mephenytoin (S/R ratio). The results were as follows: 0.0269 0.0400 0.0550 0.0550 0.0650 0.0670 0.0700 0.0720 0.0760 0.0850 0.0870 0.0870 0.0880 0.0900 0.0900 0.0990 0.0990 0.0990 0.0990 0.0990 0.0990 0.0990 0.0990 0.0990 0.0990 0.0990 0.0990 0.0990 0.0990 0.0990 0.0990 0.0990 0.0990 0.0990 0.0990 0.0990 0.0990 0.0990 0.0990 0.0990 0.0990 0.0990 0.0990 0.0990 0.0990 0.1000 0.1020 0.1040 0.1050 0.1050 0.1080 0.1080 0.1090 0.1090 0.1090 0.1160 0.1190 0.1200 0.1230 0.1240 0.1340 0.1340 0.1370 0.1390 0.1460 0.1480 0.1490 0.1490 0.1500 0.1500 0.1500 0.1540 0.1550 0.1570 0.1600 0.1650 0.1650 0.1670 0.1670 0.1677 0.1690 0.1710 0.1720 0.1740 0.1780 0.1780 0.1790 0.1790 0.1810 0.1880 0.1890 0.1890 0.1920 0.1950 0.1970 0.2010 0.2070 0.2100 0.2100 0.2140 0.2150 0.2160 0.2260 0.2290 0.2390 0.2400 0.2420 0.2430 0.2450 0.2450 0.2460 0.2460 0.2470 0.2540 0.2570 0.2600 0.2620 0.2650 0.2650 0.2680 0.2710 0.2800 0.2800 0.2870 0.2880 0.2940 0.2970 0.2980 0.2990 0.3000 0.3070 0.3100 0.3110 0.3140 0.3190 0.3210 0.3400 0.3440 0.3480 0.3490 0.3520 0.3530 0.3570 0.3630 0.3630 0.3660 0.3830 0.3900 0.3960 0.3990 0.4080 0.4080 0.4090 0.4090 0.4100 0.4160 0.4210 0.4260 0.4290 0.4290 0.4300 0.4360 0.4370 0.4390 0.4410 0.4410 0.4430 0.4540 0.4680 0.4810 0.4870 0.4910 0.4980 0.5030 0.5060 0.5220 0.5340 0.5340 0.5460 0.5480 0.5480 0.5490 0.5550 0.5920 0.5930 0.6010 0.6240 0.6280 0.6380 0.6600 0.6720 0.6820 Mth251 Page 2 (a) From these data construct the following distributions: frequency, relative frequency, cumulative frequency, and cumulative relative frequency; and the following graphs: histogram, frequency polygon. (b) The investigators defined as poor metabolizers of mephenytoin any subject with an S/R mephenytoin ratio greater than .9. How many and what percentage of the subjects were poor metabolizers? (c) How many and what percentage of the subjects had ratios less than .7? Between .3 and .6999 inclusive?

Answer 1

Solution:

Let class interval be 0.09 Class interval Frequency Cumulative frequency Relative Cumulative relative 0-0.0899 13 13 0.068 0.068 0.09-0.1799 75 88 0.391 0.458 0.18-0.2699 32 120 0.167 0.625 0.27-0.3599 23 143 0.120 0.745 0.36-0.4499 24 167 0.125 0.870 0.45-0.5399 11 178 0.057 0.927 0.54-0.6299 10 188 0.052 0.979 0.63-0.7199 4 192 0.021 1.000

Histogram 80 70 60 50 40 30 Frequency 20 10 0 0-0.0899 0.09-0.1799 0.18-0.2699 0.27-0.3599 0.36-0.4499 0.45-0.5399 0.54-0.6299 0.63-0.7199

Midpoint Frequency 0.04495 13 0.13495 75 0.22495 32 0.31495 23 0.40495 24 0.49495 11 0.58495 10 0.67495 4

Frequency polygon 80 70 60 50 40 Frequency 30 20 10 0 0 0.2 0.4 0.6 0.8 b) No values are greater than 0.9. Hence, zero percent C) 63 subjects had S/R values less than 0.70. i.e (63/192)= 0.3281 Therefore, 32.8125 percent had S/R in the range 0.3 -0.699