*Measure of Central Tendency
What we need in many instances is the ability to summarize the data by means of a single number called a descriptive measure. Describe measure may be computed from the data of a sample or the data of a population.
The three most commonly used measures of central tendancy are the mean, median, and the mode,
The most familiar measure of central tendancy is the arithmetic mean.
The mean is obtained by adding all the valuse in a population or sample and dividing by the number of values that are added.
Median: The median is that value of the variate for which 50% of observations, when arranged in order of magnitude lie on each side.
Mode: The mode is the value, which occurs most frequently.
*Measures Of Dispersion or Variability
The most common measures of dispersion or variability are (Range, Variance, Standard deviation, and Coefficient of variation).
Range (R): the range is the difference between the smallest and the largest values in a set of observations.
Variance: the variance is the most commonly used to measure of spread in biological statistics. For a population is defined as the sum of squares of the deviations from the mean (SS), dividing by the total number of the deviations), and by one less than the total number of the deviations (degree of freedom, df) for a sample.
Standard Deviation (s) or (sd): Is defined as a positive square root of variance
Coefficient of Variation (C.V): Is defined as the ratio of the standard deviation to the mean. It is independent of the units employed.
EXERCISES
For each of the data sets in the following excercises comput:
(a) the mean
(b) the median
(c) the mode
(d) the range
(e) the variance
(f) the standard deveation
(g) the coefficient of variation C.V
2.5.1
Thirteen patients with severe chronic airflow limitation were the subjects of a study to investigate the effectiveness of treatment to improve gas exchange in such subjects. The following are the body surface areas (m2) of the patients
2.1
1.74
1.68
1.83
1.57
1.71
1.73
1.65
1.74
1.57
2.76
1.9
1.77
ANSWER
(a) 1.8269
(b) 1.74
(c) 1.57
(d) 1.19
(e) .09807308
(f) .31316621
(g) 17.142
2.5.3
Seventeen patiients admitted to the Aberdeen Teaching Hospitals in Scotland between 1980 and mid-1988 were diagnosed as having pyogenic liver abscess. Nine of the patients died. The following are the ages of the subjects in the study:
63
72
62
69
71
84
81
78
61
79
84
67
86
69
64
87
76
ANSWER
(a) 73.52941176
(b) 72
(c) 69; 76; 84
(d) 26
(e) 76.76470588
(f) 8.761547
(g) 11.916
2.5.5
In an article in American Journal of Obstetrics and Gynecology , the reasercher discusses his study of arterial blood flow velocity waveforms of the pelvis and lower extremities in normal and growth-retarded fetuses. He states that his preliminary data suggest that" the formal artery pulsatility index cannot be used as an indicator of adverse fetal outcome, whereas absent or revers flow of the umbilical artery seems to be better correlated with adverse fetal outcome. : the following are gestational ages (in weeks) of 20 growth-retarted fetuses that he studied:
24
26
27
28
28
28
29
30
30
31
32
32
33
33
34
34
35
35
35
36
ANSWER
(a) 31
(b) 31.5
(c) 28; 35
(d) 12
(e) 11.78947368
(f) 3.4335803
(g) 11.076