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

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



Answer :

To determine which histogram represents Blanca's lap times over the course of three days, we need to consider all the lap times combined together. Here's a detailed step-by-step approach:

1. List the Lap Times for Each Day:
- Day 1 Lap Times (in seconds): 83, 92, 91, 89, 94, 93, 88, 84
- Day 2 Lap Times (in seconds): 87, 90, 92, 91, 92, 95, 90, 85
- Day 3 Lap Times (in seconds): 85, 86, 91, 93, 91, 89, 88, 84

2. Combine the Lap Times from All Days:
- Collect all the lap times into a single list to find the frequency of each time or range of times.

```
Combined Lap Times (in seconds):
83, 92, 91, 89, 94, 93, 88, 84,
87, 90, 92, 91, 92, 95, 90, 85,
85, 86, 91, 93, 91, 89, 88, 84
```

3. Organize the Lap Times:
- To aid in creating a histogram, let's count the frequency of each lap time by grouping them into ranges (bins). For this example, we can use an interval of 2 seconds per bin:

[tex]\[ \begin{array}{|c|c|} \hline \text{Range (sec)} & \text{Frequency} \\ \hline 83-84 & 3 \\ 85-86 & 3 \\ 87-88 & 3 \\ 89-90 & 4 \\ 91-92 & 6 \\ 93-94 & 3 \\ 95-96 & 1 \\ \hline \end{array} \][/tex]

4. Create the Histogram:
- Using the above frequencies, we can draw the histogram:

```
Number of Laps
Frequency
|
|
|

|
|

|

|

|

|-----------------------------
83-84 85-86 87-88 89-90 91-92 93-94 95-96
```

- Interpret the histogram:
- The highest frequency is in the 91-92 second range with 6 laps.
- Both the 89-90 and 83-84 ranges have 4 and 3 laps respectively.
- The lowest frequency is in the 95-96 second range with 1 lap.

This detailed breakdown reveals the correct histogram representing Blanca's lap times from her three days of practice.