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]
