Total Body Calcium and Prednisolone Treatment

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STATISTICS

Answer THREE questions in total. ONE question from SECTION A and TWO questions from SECTION B.

SECTION A

Question A1
The total body calcium (expressed as a percentage of the mean normal value) was determined for a random sample of 60 rheumatoid arthritis patients receiving prednisolone treatment and results are tabulated below.
Total Body Calcium (%)
85 80 90 81 76 67
77 85 81 83 75 80
86 82 78 82 71 66
81 90 82 80 76 69
79 74 80 80 81 83
83 86 85 81 80 93
80 78 73 83 83 80
79 84 83 82 83 81
77 86 80 79 78 91
74 74 85 88 80 96

(a) Using a tally mark count, construct a frequency distribution table for these results based on classes of width 5 and beginning with the class with lower class boundary 65. [20%]
Class Interval Freq (f)
65<=x<70 3
70<=x<75 5
75<=x<80 11
80<=x<85 28
85<=x<90 8
90<=x<95 4
95<=x<100 1
Sum = 60

(b) Using this frequency distribution table, plot the ogive and hence produce graphical estimates of the median and quartiles of total body calcium of these rheumatoid arthritis patients. [30%]
Class Interval Freq (f) End Point Cu. Freq
65<=x<70 3 70 3
70<=x<75 5 75 8
75<=x<80 11 80 19
80<=x<85 28 85 47
85<=x<90 8 90 55
90<=x<95 4 95 59
95<=x<100 1 100 60
Sum = 60

Median = 81
First Quartile = 78
Second Quartile = 81
Third Quartile = 83
Fourth Quartile = 96

(c) Using this frequency distribution table, and employing a suitable coding technique, calculate the mean and variance of this sample of total body calcium determinations. [50%]
Class Interval Freq (f) Mid Point (x) (f)*(x) x^2 f*x^2
65<=x<70 3 67.5 202.5 4556.25 13668.75
70<=x<75 5 72.5 362.5 5256.25 26281.25
75<=x<80 11 77.5 852.5 6006.25 66068.75
80<=x<85 28 82.5 2310 6806.25 190575
85<=x<90 8 87.5 700 7656.25 61250
90<=x<95 4 92.5 370 8556.25 34225
95<=x<100 1 97.5 97.5 9506.25 9506.25
Sum = 60 4895 401575

Mean =
Standard Deviation =
Question A2
In a recent study of coastal pollution, the amount of lead absorbed by the seaweed Fucus spiralis was determined. This seaweed species tends to grow at the high-water mark and is therefore exposed for most of the time. Levels of lead were measured in g Pb (dry weight) and results are tabulated below.
Levels of lead in Fucus ...