in the data set below, what is the upper quartile? 1 1 1 3 4 6

Explanation:

Step1: Arrange data in order

The data 1, 1, 1, 3, 4, 6 is already in ascending - order.

Step2: Calculate position of upper - quartile

The formula to find the position of the upper - quartile ($Q_3$) for a data set of size $n$ is $Q_3$ position $=\frac{3(n + 1)}{4}$. Here, $n = 6$. So, $Q_3$ position $=\frac{3\times(6 + 1)}{4}=\frac{3\times7}{4}=5.25$.

Step3: Interpolate to find $Q_3$

The 5th value is 4 and the 6th value is 6. Using interpolation: $Q_3=4+(6 - 4)\times0.25=4 + 0.5=4.5$.

Answer:

4.5