6-13
Center Point Center Point
(2) When Frequency includes decimal fraction values
The Q1, Q3 and Med values for this calculation method are described below.
Q1 = {value of element whose cumulative frequency ratio is greater than 0.25 and nearest to
0.25}
When the cumulative frequency ratio for some data value is exactly 0.25, Q1 is the average of
that data value and the next data value.
Q3 = {value of element whose cumulative frequency ratio is greater than 0.75 and nearest to
0.75}
When the cumulative frequency ratio for some data value is exactly 0.75, Q3 is the average of
that data value and the next data value.
Med = {value of element whose cumulative frequency ratio is greater than 0.5 and nearest to
0.5}
When the cumulative frequency ratio for some data value is exactly 0.5, Med is the average of
that data value and the next data value.
The following shows an actual example of the above.
Data Value Frequency
Cumulative
Frequency
Cumulative
Frequency Ratio
1 0.1 0.1 0.1/1.0 = 0.1
2 0.1 0.2 0.2/1.0 = 0.2
3 0.2 0.4 0.4/1.0 = 0.4
4 0.3 0.7 0.7/1.0 = 0.7
5 0.1 0.8 0.8/1.0 = 0.8
6 0.1 0.9 0.9/1.0 = 0.9
7 0.1 1.0 1.0/1.0 = 1.0
• 3 is the value whose cumulative frequency ratio is greater than 0.25 and nearest to 0.25, so
Q1 = 3.
• 5 is the value whose cumulative frequency ratio is greater than 0.75 and nearest to 0.75, so
Q3 = 5.
• 4 is the value whose cumulative frequency ratio is greater than 0.5 and nearest to 0.5, so
Med = 4.
Median
1 234567 98
= Q1
2
2
+
3
= Q3
2
7
+
8
Median
1 234567 98
= Q1
2
2
+
3
= Q3
2
7
+
8
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