in the data set below, what is the upper quartile? 18 19 38 69 73 75 77 85
in the data set below, what is the upper quartile? 18 19 38 69 73 75 77 85
Answer
Answer:
76
Explanation:
Step1: Calculate position
The formula for the position of the upper - quartile ($Q_3$) for a data set of size $n$ is $i=\frac{3(n + 1)}{4}$. Here, $n = 8$, so $i=\frac{3\times(8 + 1)}{4}=\frac{3\times9}{4}=6.75$.
Step2: Interpolate
Since the position is not an integer, we interpolate between the 6th and 7th ordered data - values. The 6th value is 75 and the 7th value is 77. Using the interpolation formula $Q_3=x_{j}+(i - j)(x_{j + 1}-x_{j})$, where $j = 6$, $x_{j}=75$, $x_{j + 1}=77$, and $i = 6.75$. So $Q_3=75+(6.75 - 6)\times(77 - 75)=75+0.75\times2=75 + 1.5=76$.