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

  

(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

a) For calculating frequency, relative frequency, cumulative frequency and cumulative relative frequency we use Ms-Excel and formulae for these are as follows,

• Frequency: The number of times a value of the data occurs.
• Relative Frequency: The ratio of the number of times a value of the data occurs in the set of all outcomes to the number of all outcomes.
• Cumulative Frequency: The Cumulative Frequency is the sum of the frequencies for all values that are less than or equal to the given value.
• Cumulative Relative Frequency: The term applies to an ordered set of observations from smallest to largest. The Cumulative Relative Frequency is the sum of the relative frequencies for all values that are less than or equal to the given value.

Also for drawing frequency polygon and histogram we use Ms-Excel.

I have attached the images of all above calculations.

b) By observing all the data, none of the S/R ratio is greater than 0.9.

By observing data, 100% observations are less than 0.7.

And 56 observations lise in between 0.3 and 0.699.