To determine which histogram represents Blanca's lap times for the three days of practice, follow these steps:
1. Collect all Lap Times:
Combine the lap times from all three days into one list. Based on the provided table:
- Day 1 Lap Times: 83, 92, 91, 89, 94, 93, 88, 84
- Day 2 Lap Times: 87, 90, 92, 91, 92, 95, 90, 85
- Day 3 Lap Times: 85, 86, 91, 93, 91, 89, 88, 84
Combining them:
[tex]\[
\text{All Lap Times} = [83, 92, 91, 89, 94, 93, 88, 84, 87, 90, 92, 91, 92, 95, 90, 85, 85, 86, 91, 93, 91, 89, 88, 84]
\][/tex]
2. Create a Histogram:
To create a histogram, we need to establish bins (intervals) to categorize the lap times. Let's use bins with a width of 2 seconds starting from 80 seconds up to 98 seconds:
- Bins: 80–82, 82–84, 84–86, 86–88, 88–90, 90–92, 92–94, 94–96, 96–98
3. Count the Frequencies for Each Bin:
Count the number of lap times falling within each bin category:
- 80–82: 0
- 82–84: 1 (lap time 83)
- 84–86: 4 (lap times 84, 84, 85, 85)
- 86–88: 2 (lap times 86, 87)
- 88–90: 4 (lap times 88, 88, 89, 89)
- 90–92: 6 (lap times 90, 90, 91, 91, 91, 91)
- 92–94: 5 (lap times 92, 92, 92, 93, 93)
- 94–96: 2 (lap times 94, 95)
- 96–98: 0
Therefore, the histogram is represented by the following frequencies:
[tex]\[
\text{Frequencies} = [0, 1, 4, 2, 4, 6, 5, 2, 0]
\][/tex]
4. Histogram Representation:
The histogram can now be represented as follows:
- Bin (Seconds): Frequency
- 80–82: 0
- 82–84: 1
- 84–86: 4
- 86–88: 2
- 88–90: 4
- 90–92: 6
- 92–94: 5
- 94–96: 2
- 96–98: 0
This histogram accurately represents Blanca's lap times over the three days of practice. It visually shows the distribution of her lap times across the specified bins. The histogram can be plotted on a graph where the x-axis represents the bins (seconds) and the y-axis represents the frequency of lap times in each bin.
