Finding the Median of the Dataset

The median is the middle value in a dataset that is ordered from least to greatest. It is a measure of central tendency.

To find the median, we first need to arrange the data in ascending or descending order. The given dataset is:

3, 3, 7, 8, 12, 13, 16, 19

The data is already sorted in ascending order.

Next, we count the number of data points in the dataset. Let 'n' be the number of data points.

• The number of data points, n = 8.

Since 'n' (8) is an even number, the median is the average of the two middle terms. The positions of the two middle terms are the \( \left(\frac{n}{2}\right)^{\text{th}} \) term and the \( \left(\frac{n}{2} + 1\right)^{\text{th}} \) term.

• \( \left(\frac{n}{2}\right)^{\text{th}} \) term = \( \left(\frac{8}{2}\right)^{\text{th}} \) term = 4th term
• \( \left(\frac{n}{2} + 1\right)^{\text{th}} \) term = \( \left(\frac{8}{2} + 1\right)^{\text{th}} \) term = \( (4 + 1)^{\text{th}} \) term = 5th term

Now, we identify the 4th and 5th terms in the sorted dataset:

3, 3, 7, 8, 12, 13, 16, 19

• The 4th term is 8.
• The 5th term is 12.

The median is the average of these two terms:

\( \text{Median} = \frac{\text{4th term} + \text{5th term}}{2} \)

\( \text{Median} = \frac{8 + 12}{2} \)

\( \text{Median} = \frac{20}{2} \)

\( \text{Median} = 10 \)

Therefore, the median of the given dataset is 10.