Arrange the Data in Ascending Order

To find the median, first write the given numbers in order from smallest to largest.

$\text{Sorted Data: } 52, 68, 88, 90, 110, 134, 152, 180$

Determine the Number of Observations

Count the total number of terms $N$ in the data set.

$N = 8 \quad (\text{an even number})$

Apply the Median Formula for Even N

When $N$ is even, the median is the arithmetic mean of the $\left(\frac{N}{2}\right)^{\text{th}}$ and $\left(\frac{N}{2} + 1\right)^{\text{th}}$ terms.

$\frac{N}{2} = 4^{\text{th}} \text{ term} = 90, \quad \left(\frac{N}{2} + 1\right) = 5^{\text{th}} \text{ term} = 110$

Calculate the Final Median

Take the average of the $4^{\text{th}}$ and $5^{\text{th}}$ terms.

$\text{Median} = \frac{90 + 110}{2} = \frac{200}{2} = 100$