Question

in the data set below, what is the upper quartile? 1 3 3 5 6 6 8

Explanation:

Step1: Determine the number of data points

The data - set is 1, 3, 3, 5, 6, 6, 8. The number of data points $n = 7$.

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 $Q_3$ position $=\frac{3(n + 1)}{4}$. Substitute $n = 7$ into the formula: $\frac{3\times(7 + 1)}{4}=\frac{3\times8}{4}=6$.

Step3: Find the upper - quartile

Since the position is an integer (6), the upper - quartile is the 6th value in the ordered data - set. The 6th value in the ordered data - set 1, 3, 3, 5, 6, 6, 8 is 6.

Answer:

6