17 Statistics
� Relationship between frequencies and cumulative frequencies : Data
Frequency
Data less than or equal to
Cumulative frequency
10 |
f
1
|
10
|
f
1
|
20 |
f
2
|
20 |
f1� f2 |
30 |
f
3
|
30 |
f1
� f2
� f3
|
� Measures of central tendency for a data set { x1 , x2, x3, , x } arranged in ascending order : x1 � x2 � x3 � � xn 1 . x �
: Mean n 2 . The datum or the average value of two data at the middle : Median 3 . The datum appears the most : Mode
� |
Measures of dispersion for a data set
{ x1 , x2, x3,
|
, x n
} arranged in ascending
|
|
order : |
|
1 . xn � x1
: Range
2 . Two subgroups A and B can be formed from the data set such that all data of the subgroup A are less than or equal to the median , while all data of the subgroup B are greater than or equal to the median
3 . Q1
� The median of the subgroup A : Lower quartile
4 . Q3
� The median of the subgroup B : Upper quartile
5 . Q3� Q1: Inter-quartile range ( IQR )
n
6 . |
� � |
|
( x
� x)
|
�
( x
|
� x) |
�
( x
� x)
|
� |
�
( x
|
� x) |
|
|
|
n |
|
|
|
2 2 2 2 1 2 3 n
|
: Standard deviation |
� Box-and-whisker diagram :
� A datum x is defined to be an outlier if x�Q1 � 1.5IQR or x�Q3 � 1.5IQR
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