SHEN’S CLASS NOTES
1
Chapter 9
Medians and Order Statistics
Suppose
a
1
<
a
2
<
a
3
< … <
a
n
are
n
numbers.
a
1
is called the first order statistics (or, the minimum number).
a
2
is called the second order statistics (the 2nd smallest number).
……
a
i
is called the
ith
order statistics (the
ith
smallest number).
a
n
is called the
nth
order statistics (also the maximum number).
If
n
is an odd number then
the index
i
= (
n
+1)/2 is the midpoint and
a
i
= a
(
n
+1)/2
is called the median.
If
n
is an even number then
a
i
= a
⎣
(
n
+1)/2
⎦
is called the lower median, and
a
i
= a
⎡
(
n
+1)/2
⎤
is called the upper median.

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