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Total Body Calcium and Prednisolone Treatment

Answer THREE questions in total. ONE question from SECTION A and TWO questions from SECTION B. The solutions have to be typed not scanned.

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%]
(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%]
(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%]

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 spiralis
15.1 11.9 13.0 15.6 10.9 14.0 16.3
13.0 14.6 13.7 14.6 13.0 12.2 13.4

(a) Plot these results on Normal probability graph paper and hence describe the evidence that these results are Normally distributed. [50%]

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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 ...

Solution Summary

The total body calcium and prednisoline treatment results are examined. Frequency distribution tables and suitable coding techniques are determined.

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