Questions: Calculate the median of the data shown, to two decimal places x 26.3 29.8 25.1 15.4 27.3 17.7

Transcript text: Calculate the median of the data shown, to two decimal places \begin{tabular}{|c|} \hline $\mathbf{x}$ \\ \hline 26.3 \\ \hline 29.8 \\ \hline 25.1 \\ \hline 15.4 \\ \hline 27.3 \\ \hline 17.7 \\ \hline \end{tabular}

Solution

Solution Steps

Step 1: Arrange the data in ascending order

The given data is: \[ 26.3, 29.8, 25.1, 15.4, 27.3, 17.7 \] Arranging the data in ascending order: \[ 15.4, 17.7, 25.1, 26.3, 27.3, 29.8 \]

Step 2: Determine the number of data points

The number of data points is $ n = 6 $, which is even.

Step 3: Calculate the median

For an even number of data points, the median is the average of the $ \frac{n}{2} $-th and $ \left(\frac{n}{2} + 1\right) $-th values. Here, $ \frac{n}{2} = 3 $ and $ \frac{n}{2} + 1 = 4 $. Thus, the median is the average of the 3rd and 4th values: \[ \text{Median} = \frac{25.1 + 26.3}{2} = \frac{51.4}{2} = 25.7 \]

Final Answer

\[ \boxed{25.7} \]

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