Answer:
The upper quartile is 7.5.
Step-by-step explanation:
Given : Data - 27, 5, 11, 13, 10, 8, 14, 18, 7
To find : The upper quartile of the data ?
Solution :
Arrange the data from least to greatest,
5, 7, 8, 10, 11, 13, 14, 18, 27
First we find the median of the data.
As number of terms 9 is odd the median is [tex]\frac{n+1}{2}[/tex] th term,
[tex]\frac{n+1}{2}=\frac{9+1}{2}=5[/tex]th term
The 5th term of data is median is 11.
Before 11 is the data range of upper quartile.
i.e. data - 5, 7, 8, 10
Now, The upper quartile is the median of the upper quartile range.
Median of even term is given by, [tex]\frac{1}{2}(\frac{n}{2}th+\frac{n}{2}+1)th[/tex]
[tex]\frac{1}{2}(\frac{4}{2}th+\frac{4}{2}+1)th=\frac{1}{2}(2nd+3rd)[/tex]
[tex]m=\frac{1}{2}(7+8)[/tex]
[tex]m=\frac{1}{2}(15)[/tex]
[tex]m=7.5[/tex]
The upper quartile is 7.5.
