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Blanca runs 8 laps around the track each day to train for an endurance race. She times each lap to practice her pacing for the race. The table shows the lap times, in seconds, for three days of practice.

Endurance Race Training

\begin{tabular}{|c|c|c|c|c|c|c|c|c|}
\hline
\textbf{Day 1 Lap Times (seconds)} & 83 & 92 & 91 & 89 & 94 & 93 & 88 & 84 \\
\hline
\textbf{Day 2 Lap Times (seconds)} & 87 & 90 & 92 & 91 & 92 & 95 & 90 & 85 \\
\hline
\textbf{Day 3 Lap Times (seconds)} & 85 & 86 & 91 & 93 & 91 & 89 & 88 & 84 \\
\hline
\end{tabular}

Which histogram represents Blanca's lap times for the three days of practice?

Histogram Options:
1. ...
2. ...
3. ...
4. ...

Sagot :

To represent Blanca's lap times for the three days of practice with a histogram, we need to follow several steps involving the combination of data and distribution of that data into bins. Here is a detailed step-by-step solution to derive the necessary histogram:

1. Combine All Lap Times:
- For Day 1: [83, 92, 91, 89, 94, 93, 88, 84]
- For Day 2: [87, 90, 92, 91, 92, 95, 90, 85]
- For Day 3: [85, 86, 91, 93, 91, 89, 88, 84]

Combining these lists together, we get:
```
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]
```

2. Define Bins for the Histogram:
To cover the range of lap times, we choose the following bins:
```
bins = [80, 82, 84, 86, 88, 90, 92, 94, 96]
```

3. Count Lap Times in Each Bin:
The bins will now be used to count the number of lap times that fall into each range:
- Bin [80, 82): 0 laps
- Bin [82, 84): 1 lap
- Bin [84, 86): 4 laps
- Bin [86, 88): 2 laps
- Bin [88, 90): 4 laps
- Bin [90, 92): 6 laps
- Bin [92, 94): 5 laps
- Bin [94, 96): 2 laps

Therefore, the histogram counts are:
```
histogram = [0, 1, 4, 2, 4, 6, 5, 2]
```

4. Edges of Each Bin:
The edges of the bins are:
```
bin_edges = [80, 82, 84, 86, 88, 90, 92, 94, 96]
```

Given these counts and bin edges, our final histogram would look as follows:
- Bin 80-82: 0 laps
- Bin 82-84: 1 lap
- Bin 84-86: 4 laps
- Bin 86-88: 2 laps
- Bin 88-90: 4 laps
- Bin 90-92: 6 laps
- Bin 92-94: 5 laps
- Bin 94-96: 2 laps

This representation matches the numerical result achieved, confirming that it is accurate. Thus, the correct histogram for Blanca's lap times over the three days is represented by:

[tex]\[ \begin{array}{|c|c|c|c|c|c|c|c|c|} \hline \text{Bin Range} & 80-82 & 82-84 & 84-86 & 86-88 & 88-90 & 90-92 & 92-94 & 94-96 \\ \hline \text{Counts} & 0 & 1 & 4 & 2 & 4 & 6 & 5 & 2 \\ \hline \end{array} \][/tex]
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