https://file.aiquickdraw.com/mathbot/file/1726038390690q58gpu3l.jpg

https://file.aiquickdraw.com/mathbot/file/1726038390692gtywrn9z.jpg

Using this table answer the another image 

Let's first analyze the two images and the provided data to help answer the questions.

### Data from the table:
- The first image shows a list of fastest 1500m Women's running times at various Olympic years, converted from minutes and seconds to seconds.
  
  The conversion formula for converting minutes and seconds to just seconds is:
  \[
  \text{{Total seconds}} = \text{{minutes}} \times 60 + \text{{seconds}}
  \]

Here’s a review of the table entries:
| Olympic Year | Fastest Time (Minutes and Seconds) | Fastest Time (Seconds) |
|--------------|-----------------------------------|------------------------|
| 1984         | 3m 32.52s                         | 212.52s                |
| 1988         | 3m 35.96s                         | 215.40s                |
| 1992         | 3m 32.52s                         | 212.52s                |
| 1996         | 3m 35.78s                         | 215.78s                |
| 2000         | 3m 32.07s                         | 212.07s                |
| 2004         | 3m 34.18s                         | 214.18s                |
| 2008         | 3m 33.11s                         | 213.11s                |
| 2012         | 3m 34.08s                         | 214.08s                |
| 2016         | 3m 50.00s                         | 230.00s                |
| 2020         | 3m 28.32s                         | 208.32s                |
| 2024         | 3m 27.65s                         | 207.65s                |

---

### Answering the questions:

#### i) What type of data do the 1500m run times represent?

- **Answer**: The 1500m run times represent **continuous quantitative data**, as these times can take on any value within a given range and are measurable in time.

#### ii) What type of data does the year of the Olympics represent?

- **Answer**: The year of the Olympics represents **discrete quantitative data**, as these are specific points in time (years) that can only take certain values (whole numbers).

#### iii) Calculate the average time of the 1500m women's running race over the years collected.

To calculate the average time, sum up all the race times (in seconds) and divide by the total number of years.

\[
\text{Average time} = \frac{\text{Sum of all times}}{\text{Number of times}}
\]

Now, summing the race times:
\[
212.52 + 215.40 + 212.52 + 215.78 + 212.07 + 214.18 + 213.11 + 214.08 + 230.00 + 208.32 + 207.65 = 2,355.63 \, \text{seconds}
\]

The number of times is 11.

\[
\text{Average time} = \frac{2,355.63}{11} = 214.15 \, \text{seconds}
\]

The average time is approximately **214.15 seconds**.

#### iv) What is the range of the 1500m women's race times across the eleven Olympics?

The range is the difference between the maximum and minimum race times.

- Maximum time: 230.00 seconds (2016)
- Minimum time: 207.65 seconds (2024)

\[
\text{Range} = 230.00 - 207.65 = 22.35 \, \text{seconds}
\]

The range is **22.35 seconds**.

---

Would you like further clarification or details? Here are five related questions you could explore:

1. What is the median time for the 1500m race across these years?
2. How much faster is the fastest recorded time (2024) compared to the slowest (2016)?
3. How has the performance trend changed over the years (i.e., faster or slower)?
4. Can we predict the next Olympic time based on this data?
5. What could cause such a significant difference between the fastest and slowest times?

**Tip**: When working with continuous data like race times, creating a graph (such as a line plot) can help visualize trends easily!

Using this table, answer the questions in the other image.

Learn how to analyze the 1500m women's race times over multiple Olympic years using key statistical methods. This problem covers converting times to seconds, calculating averages, and determining the range of data. Suitable for students in Grades 9-12.

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