Biostatistics for Animal Science

8 Biostatistics for Animal Science
The Median of a sample of n observations y1,y2,...,yn is the value of the observation that is in
the middle when observations are sorted from smallest to the largest. It is the value of the
observation located such that one half of the area of a histogram is on the left and the other
half is on the right. If n is an odd number the median is the value of the (n+1) /2-th
observation. If n is an even number the median is the average of (n) /2-th and (n+2) /2-th
observations.
The Mode of a sample of n observations y1,y2,...,yn is the value among the observations that
has the highest frequency.
Figure 1.4 presents frequency distributions illustrating the mean, median and mode.
Although the mean is the measure that is most common, when distributions are asymmetric,
the median and mode can give better information about the set of data. Unusually extreme
values in a sample will affect the arithmetic mean more than the median. In that case the
median is a more representative measure of central tendency than the arithmetic mean. For
extremely asymmetric distributions the mode is the best measure.
frequency
mean
(balance point)
frequency
50% 50% frequency
median
Figure 1.4 Interpretation of mean, median and mode
1.4.3 Measures of Variability
mode
maximum
Commonly used measures of variability are the range, variance, standard deviation and
coefficient of variation.
Range is defined as the difference between the maximum and minimum values in a set of
observations.
Sample variance (s 2 ) of n observations (measurements) y1, y2,...,yn is:
2
( − )
2
=
− 1
∑ y y
i i
s
n
This formula is valid if y is calculated from the same sample, i.e., the mean of a population
is not known. If the mean of a population (µ) is known then the variance is:
∑ y
i i
s
n
−
2
( µ
)
2
=