Biol 3000-biostatistics le-2017-2018.calstatela.edu/pluginfile.php/1585196/mod_r
ID: 3044073 • Letter: B
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Biol 3000-biostatistics le-2017-2018.calstatela.edu/pluginfile.php/1585196/mod_resource/content/10/Homework1.pdf Biology 3000, Biometrics Homework #1 Answer each question and show intermediate calculations. Please be neat! Do the work with a hand calculator by yourself. Afier all, that's the way you'll need to do it during an exam Total serum protein levels were measured for 12 adults: Total Serum Protein (g/dL) 6.97.5 7.0 8.0 7.7 7.0 8.4 7.3 7.1 72 7.5 6.0 Compute the arithmetic mean, geometric mean, harmonic mean, and median for these data to two decimal places. (6 points) Compute the standard deviation, mean deviation, range, and coefficient of variation (as a percentage) to two decimal places. (6 points) 1. 2. 3. Compute the 20, 50h, and 75h percentiles to two decimal places. (3 points) 4. Data were collected on the number of hospitalstay's per 65 year-old adult during the previous five years. The data appear below. Hospital Stays per 5 Year Period Number of hospital stays Number of adults 552 288 90 14 56 89 15 Compute the mean, median, standard deviation, and coefficient of variation (as a decimal number) for the number of hospital stays per adult to two decimal places. (5 points) MacBook AiExplanation / Answer
1.
From this we can find Mean = sum/count
= 87.6/12 = 7.3
2.
Now subtracting mean from each reading and taking square we get
Variance = sum((SP-Mean)^2)/count
= (0.16+...+0.01+0)/12Thus. variance = 4.02/12 = 0.335
standard deviation = sqrt(variance) = sqrt(0.335)
=0.58
coefficient of variation =(standard deviation/Mean)*100 %
= (0.58/7.3) * 100 %
= 7.94%
To calculate mean deviation = sum of modulus of all distances from mean/count
Thus, Mean deviation = (0.4+..+0.2)/12 = 5.2/12 = 0.43
3.
Formula for percentile = p(n+1) /100
where, p = pth percentile
n = number of data values
Here n =12 (12 values are given)
arranging in ascending order we get
Thus,
20th percentile => (20*13/100)th element
=> 2.6 th element
= 2nd element + 0.6*(3rd-2nd element)
= 6.9 + 0.6(7-6.9)
= 6.96
50th percentile = (50*13/100)th element = 6.5th element
= 6th + 0.5(7th-6th)
= 7.2 - 0.5(7.5-7.2)
= 7.35
75th percentile = (75*13/100)th element = 9.75th element
= 9th + 0.75(10th-9th)
= 7.5 - 0.75(7.7-7.5)
= 7.65
4.
For data given use the same formulaes used in above example to obtain answer
Serial no 1 2 3 4 5 6 7 8 9 10 11 12 Sum Mean SerumProtein(SP) 6.9 7.5 7 8 7 7.3 6 7.7 8.4 7.1 7.2 7.5 87.6 7.3
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