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STATISTICS FORMULAE
Descriptive Statistics for Grouped Data
•
Mean:
¯
x
=
k
i
=1
f
i
x
i
n
•
Median:
=
L
+
1
f
1
2
k
i
=1
f
i
−
F
×
C
•
Mode:
=
L
+
λ
1
λ
1
+
λ
2
×
C
•
Population variance:
σ
2
=
1
N
k
i
=1
f
i
x
2
i
−
1
N
k
i
=1
f
i
x
i
2
•
Sample variance:
s
2
=
1
n
−
1
k
i
=1
f
i
x
2
i
−
1
n
k
i
=1
f
i
x
i
2
•
Quartiles:
Q
i
=
L
+
1
f
Q
i
i
4
n
−
F
×
C
where
i
= 1
,
2
,
3
,
4
•
Deciles:
D
i
=
L
+
1
f
D
i
i
10
n
−
F
×
C
where
i
= 1
,
2
,
3
, . . . ,
10
•
Percentiles:
P
i
=
L
+
1
f
P
i
i
100
n
−
F
×
C
where
i
= 1
,
2
,
3
, . . . ,
100
Outlier
•
x < Q
1
−
1
.
5(
Q
3
−
Q
1
)
and
x > Q
3
+ 1
.
5(
Q
3
−
Q
1
)
1