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Rae and Doris are training to swim a 200-meter freestyle race. The table lists their practice times during training camp.

\begin{tabular}{|c|c|}
\hline
\begin{tabular}{c}
Rae's Times \\
(minutes)
\end{tabular} & \begin{tabular}{c}
Doris's Times \\
(minutes)
\end{tabular} \\
\hline 2.12 & 2.32 \\
\hline 2.01 & 2.19 \\
\hline 2.46 & 2.26 \\
\hline 2.00 & 2.03 \\
\hline 2.22 & 2.11 \\
\hline 2.31 & 2.14 \\
\hline 2.23 & 2.07 \\
\hline
\end{tabular}

The median of Rae's data is [tex]$\square$[/tex] minutes, and the median of Doris' data is [tex]$\square$[/tex] minutes. The interquartile range for Rae is [tex]$\square$[/tex], and the interquartile range for Doris is [tex]$\square$[/tex]. The two data sets overlap [tex]$\square$[/tex].



Answer :

GinnyAnswer
Let’s analyze the data for Rae and Doris.

1. Median Calculation:

The median is the middle value of a data set when the values are sorted. If there's an odd number of observations, the median is the middle number. If there's an even number, it's the average of the two middle numbers.

- Rae's Times (in sorted order): 2, 2.01, 2.12, 2.22, 2.23, 2.31, 2.46
- Median: 2.22 minutes (middle value)

- Doris's Times (in sorted order): 2.03, 2.07, 2.11, 2.14, 2.19, 2.26, 2.32
- Median: 2.14 minutes (middle value)

2. Interquartile Range (IQR):

The IQR is the difference between the first quartile (Q1) and the third quartile (Q3). Q1 is the median of the lower half, and Q3 is the median of the upper half.

- Rae's Times:
- Q1 (25th percentile): 2.12 minutes
- Q3 (75th percentile): 2.325 minutes
- IQR: 2.325 - 2.12 = 0.205 minutes

- Doris's Times:
- Q1 (25th percentile): 2.07 minutes
- Q3 (75th percentile): 2.205 minutes
- IQR: 2.205 - 2.07 = 0.135 minutes

3. Overlap Determination:

Data sets overlap if there is at least one value that lies within the range of the other data set.

- Rae’s range: [2.00, 2.46]
- Doris’s range: [2.03, 2.32]

Since there are times in Rae's data that overlap with the range of Doris's times (2.03 is within Rae’s and Doris’s range), the two data sets do overlap.

Final Answers:

- The median of Rae's data is: 2.22 minutes
- The median of Doris's data is: 2.14 minutes
- The interquartile range for Rae is: 0.205 minutes
- The interquartile range for Doris is: 0.135 minutes
- The two data sets overlap: True

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