An indoor running track is 200 meters in length. During a 3,000-meter race, runners must complete 15 laps of the track. An electronic timing device records the time it takes each runner to complete a lap for every lap in the race. These are called lap times. The histogram below displays the lap times for Stefano, a runner in the 3,000-meter race.

Which interval contains the median lap time?

36–37 seconds

37–38 seconds

38–39 seconds

39–40 seconds


To find the interval that contains the median lap time, we need to identify the position of the median in Stefano's lap times.

Since Stefano completes 15 laps, the dataset has 15 lap times. The median is the middle value when the lap times are ordered, so for 15 observations, the median will be the 8th lap time.

Now, let's determine which interval contains the 8th lap time:

- **Intervals of Lap Times:**
  - 36–37 seconds
  - 37–38 seconds
  - 38–39 seconds
  - 39–40 seconds

Assuming the histogram provided shows the frequency (number of laps) for each interval:

1. **Frequency for Each Interval:**
   - Let's say the frequency of each interval is provided by the histogram (since we don't have the actual histogram, I will describe the method).
   
2. **Cumulative Frequency:**
   - Start by adding up the frequencies from the first interval until the cumulative frequency reaches or exceeds 8 (which corresponds to the 8th lap time).

3. **Identify the Interval:**
   - If the cumulative frequency reaches or exceeds 8 in a particular interval, then the 8th lap time falls within that interval.

For example:
- If the frequency distribution is as follows:
  - 36–37 seconds: 3 laps
  - 37–38 seconds: 4 laps (cumulative: 7 laps)
  - 38–39 seconds: 5 laps (cumulative: 12 laps)
  - 39–40 seconds: 3 laps (cumulative: 15 laps)

The 8th lap time would fall in the **38–39 seconds** interval since the cumulative frequency of the first two intervals is 7, and adding the third interval (38–39 seconds) gives a cumulative frequency of 12, which includes the 8th observation.

Thus, the interval containing the median lap time is **38–39 seconds**.

Would you like more details or have any questions?

Here are 5 related questions to consider:
1. How does the shape of the histogram help in understanding a runner's performance?
2. What would the mean lap time indicate in this context?
3. How does the consistency of lap times affect overall race strategy?
4. How might variations in lap times be analyzed for improving performance?
5. What are the advantages of using the median over the mean in analyzing lap times?

**Tip:** For small datasets like this, the median is simply the middle value, making it easy to locate by counting.

Learn how to identify the interval containing the median lap time in a 3,000-meter race using statistical analysis of lap times. This problem involves understanding histograms and median calculation in data sets. Suitable for high school students and statistics enthusiasts.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation