in the data set below, what is the upper quartile? 2 5 5 7 8 9
in the data set below, what is the upper quartile? 2 5 5 7 8 9
Answer
Explanation:
Step1: Arrange data in order
The data set 2, 5, 5, 7, 8, 9 is already in ascending - order.
Step2: Calculate the position of the upper quartile
The formula to find the position of the upper quartile ($Q_3$) for a data set of size $n$ is $Q_3=\frac{3(n + 1)}{4}$. Here, $n = 6$. So, $Q_3=\frac{3\times(6 + 1)}{4}=\frac{3\times7}{4}=5.25$.
Step3: Interpolate to find $Q_3$
The 5th value is 8 and the 6th value is 9. Using linear interpolation: $Q_3=8+(9 - 8)\times0.25=8 + 0.25=8.25$.
Answer:
$8.25$