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When
n
is an odd number, using the median of the total population as the reference, the population
elements are divided into two groups: values less than the median and values greater than the median.
The median value is excluded. Q
Q
= {median of the group of (
1
Q
= {median of the group of (
3
Median = {center point of the total population}
When
n
= 1, Q
= Q
1
3
(b) When Frequency includes decimal fraction values
The Q
, Q
and Median values for this calculation method are described below.
1
3
Q
= {value of element whose cumulative frequency ratio is greater than 1/4 and nearest to 1/4}
1
When the cumulative frequency ratio for some data value is exactly 0.25, Q
value and the next data value.
Q
= {value of element whose cumulative frequency ratio is greater than 3/4 and nearest to 3/4}
3
When the cumulative frequency ratio for some data value is exactly 0.75, Q
value and the next data value.
Median = {value of element whose cumulative frequency ratio is greater than 1/2 and nearest to 1/2}
When the cumulative frequency ratio for some data value is exactly 0.5, Median is the average of that data
value and the next data value.
The following shows an actual example of the above.
Data Value
Frequency
1
2
3
4
5
6
7
• 3 is the value whose cumulative frequency ratio is greater than 1/4 and nearest to 1/4, so Q
• 5 is the value whose cumulative frequency ratio is greater than 3/4 and nearest to 3/4, so Q
• 4 is the value whose cumulative frequency ratio is greater than 1/2 and nearest to 1/2, so Median = 4.
[Q
, Q
on Data] checked (default):
1
3
The Q
, Q
and Median values for this calculation method are described below.
1
3
Q
= {value of element whose cumulative frequency ratio is greater than or equal to 1/4 and nearest to 1/4}
1
Q
= {value of element whose cumulative frequency ratio is greater than or equal to 3/4 and nearest to 3/4}
3
The following shows an actual example of the above. (Number of Elements: 10)
Data Value
Frequency
1
2
3
4
5
6
7
and Q
then become the values described below.
1
3
n
− 1)/2 items from the bottom of the population}
n
− 1)/2 items from the top of the population}
= Median = population center point.
Cumulative Frequency
0.1
0.1
0.2
0.3
0.1
0.1
0.1
Cumulative Frequency
1
1
2
3
1
1
1
0.1
0.2
0.4
0.7
0.8
0.9
1.0
1
2
4
7
8
9
10
Chapter 7: Statistics Application 142
is the average of that data
1
is the average of that data
3
Cumulative Frequency Ratio
0.1/1.0 = 0.1
0.2/1.0 = 0.2
0.4/1.0 = 0.4
0.7/1.0 = 0.7
0.8/1.0 = 0.8
0.9/1.0 = 0.9
1.0/1.0 = 1.0
= 3.
1
= 5.
3
Cumulative Frequency Ratio
1/10 = 0.1
2/10 = 0.2
4/10 = 0.4
7/10 = 0.7
8/10 = 0.8
9/10 = 0.9
10/10 = 1.0
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