At the Silver City Middle School field day, a favorite event is the obstacle course. Sophie was happy that she finished it in 62 seconds. Most of the 26 students in her class took over 60 seconds. The median time was 67 seconds, and the interquartile range was about 14 seconds. The fastest student in the class finished in 54 seconds. What is the typical obstacle course time of a student in Sophie's class?

To determine the typical obstacle course time for a student in Sophie's class, we can analyze the given statistical data. Here’s a breakdown of the information provided:

1. **Median Time**: 67 seconds.  
   The median is the middle value of a data set when it is ordered from least to greatest. This means that half of the students took less than 67 seconds, and the other half took more than 67 seconds.

2. **Interquartile Range (IQR)**: About 14 seconds.  
   The IQR measures the range of the middle 50% of the data. It is calculated as the difference between the third quartile (Q3) and the first quartile (Q1). The IQR indicates the spread of the middle half of the times, showing the variability among the middle performers.

3. **Fastest Time**: 54 seconds.  
   This is the minimum time recorded among all the students.

### Analyzing the Typical Time

The median time of 67 seconds is a strong indicator of the "typical" time for a student in the class, as it represents the middle of the dataset. Given that the majority of students took over 60 seconds and the interquartile range (IQR) is about 14 seconds, we can infer some additional details:

- **Quartiles**:  
  - **Q1 (First Quartile)**: This is the 25th percentile, meaning 25% of the students finished the course faster than this time. Since the IQR is 14 seconds and the median (Q2) is 67 seconds, we can estimate Q1 to be around \( 67 - \frac{14}{2} = 67 - 7 = 60 \) seconds.
  - **Q3 (Third Quartile)**: This is the 75th percentile, meaning 75% of the students finished the course faster than this time. It can be estimated as \( 67 + \frac{14}{2} = 67 + 7 = 74 \) seconds.

- **Spread of Times**:  
  The fastest student finished in 54 seconds, which is significantly lower than the median. This suggests that there may be a few students who finished much faster than the rest, but the bulk of the students finished around the median time.

### Conclusion: Typical Obstacle Course Time

Given the median time of 67 seconds and the interquartile range (which helps us understand the spread around this median), the **typical obstacle course time for a student in Sophie's class is approximately 67 seconds**. This value best represents the central tendency of the data, showing what a typical student’s performance would be like.

Would you like more details or have any questions about this analysis?

### Relative Questions to Expand Understanding:

1. What does the interquartile range tell us about the data's spread?
2. How would the typical time change if there were outliers on either side of the median?
3. Why is the median used to describe the typical time instead of the mean?
4. How would the range of times change if the fastest time was slower than 54 seconds?
5. What additional information would be useful to further analyze the performance of students in the class?

### Tip:
Understanding the median and interquartile range can give you a clearer picture of a dataset's typical values and its variability.

Explore the typical obstacle course time for students at Silver City Middle School based on statistical analysis. Discover how median time, interquartile range, and fastest time data are used to determine the central tendency of students' performance. Suitable for high school students interested in statistics and data analysis.

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