Following the concept of a statistically convergent sequence
x
x
, we define a statistical limit point of
x
x
as a number
λ
\lambda
that is the limit of a subsequence
{
x
k
(
j
)
}
\{ {x_{k(j)}}\}
of
x
x
such that the set
{
k
(
j
)
:
j
∈
N
}
\{ k(j):j \in \mathbb {N}\}
does not have density zero. Similarly, a statistical cluster point of
x
x
is a number
γ
\gamma
such that for every
ε
>
0
\varepsilon > 0
the set
{
k
∈
N
:
|
x
k
−
γ
|
>
ε
}
\{ k \in \mathbb {N}:|{x_k} - \gamma | > \varepsilon \}
does not have density zero. These concepts, which are not equivalent, are compared to the usual concept of limit point of a sequence. Statistical analogues of limit point results are obtained. For example, if
x
x
is a bounded sequence then
x
x
has a statistical cluster point but not necessarily a statistical limit point. Also, if the set
M
:=
{
k
∈
N
:
x
k
>
x
k
+
1
}
M: = \{ k \in \mathbb {N}:{x_k} > {x_{k + 1}}\}
has density one and
x
x
is bounded on
M
M
, then
x
x
is statistically convergent.