Biostatistics

56 CHAPTER 2 DESCRIPTIVE STATISTICS
2.5.4 Standard deviation
v
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
P n
s ¼
pffiffiffiffi
u ðx i x Þ 2
t
s 2 ¼ i¼1
n 1
2.5.5 Coefficient of variation C:V: ¼ s x ð100Þ%
2.5.6 Quartile location in
ordered array
Q 1 ¼ 1 4 ðn
þ 1Þ
Q 2 ¼ 1 2 ðn
þ 1Þ
Q 3 ¼ 3 4 ðn
þ 1Þ
2.5.7 Interquartile range IQR ¼ Q 3 Q 1
2.5.8 Kurtosis
P n
ðx i x Þ 4
i¼1
Kurtosis ¼
P n
2
3 ¼
ð x Þ 2
i¼1
x i
n Pn
i¼1
ð x Þ 4
x i
ðn 1Þ 2 3
s 4
Symbol Key
C:V: ¼ coefficient of variation
IQR ¼ Interquartile range
k ¼ number of class intervals
m ¼ population mean
N ¼ population size
n ¼ sample size
ðn 1Þ ¼ degrees of freedom
Q 1 ¼ first quartile
Q 2 ¼ second quartile ¼ median
Q 3 ¼ third quartile
R ¼ range
s ¼ standard deviation
s 2 ¼ sample variance
s 2 ¼ population variance
x i ¼ i th data observation
x L ¼ largest data point
x S ¼ smallest data point
x ¼ sample mean
w ¼ class width