The table displays data collected, in meters, from a track meet.

\begin{tabular}{|l|l|l|l|}
\hline
[tex]$\frac{1}{4}$[/tex] & 6 & 2 & 4 \\
\hline
3 & [tex]$\frac{2}{3}$[/tex] & [tex]$\frac{1}{3}$[/tex] & [tex]$\frac{9}{2}$[/tex] \\
\hline
\end{tabular}

What is the median of the data collected?

A. 2.5

B. 4.5

C. 2

D. 3



Answer :

To find the median of the data collected in meters from the track meet, follow these steps carefully:

1. List the data points: First, write down all the data points provided:
- [tex]\( \frac{1}{4}, 6, 2, 4, 3, \frac{2}{3}, \frac{1}{3}, \frac{9}{2} \)[/tex]

2. Convert fractions to decimals for clarity:
- [tex]\( \frac{1}{4} = 0.25 \)[/tex]
- [tex]\( 6 \)[/tex] remains [tex]\( 6.0 \)[/tex]
- [tex]\( 2 \)[/tex] remains [tex]\( 2.0 \)[/tex]
- [tex]\( 4 \)[/tex] remains [tex]\( 4.0 \)[/tex]
- [tex]\( 3 \)[/tex] remains [tex]\( 3.0 \)[/tex]
- [tex]\( \frac{2}{3} \approx 0.6667 \)[/tex]
- [tex]\( \frac{1}{3} \approx 0.3333 \)[/tex]
- [tex]\( \frac{9}{2} = 4.5 \)[/tex]

3. Order the data points from smallest to largest:
- The data points in order are: [tex]\( 0.25, 0.3333, 0.6667, 2.0, 3.0, 4.0, 4.5, 6.0 \)[/tex]

4. Determine the number of data points:
- There are 8 data points in total, so the number [tex]\( n = 8 \)[/tex].

5. Find the median:
- Since there is an even number of data points, the median is the average of the 4th and 5th smallest numbers in the ordered list.
- The 4th smallest number is [tex]\( 2.0 \)[/tex]
- The 5th smallest number is [tex]\( 3.0 \)[/tex]

6. Calculate the median:
- The median is the average of [tex]\( 2.0 \)[/tex] and [tex]\( 3.0 \)[/tex]:
[tex]\[ \text{Median} = \frac{2.0 + 3.0}{2} = \frac{5.0}{2} = 2.5 \][/tex]

Therefore, the median of the data collected is [tex]\( 2.5 \)[/tex]. Hence, among the given options, the correct answer is:
[tex]\[ \boxed{2.5} \][/tex]