Math  /  Data & Statistics

Questioncheck camden and Logan record their resting heart rates each morning for ten days. The double line plot shows their heart rates in beats per minute. For Logan, the mean and median are 71 , the range is 8 and the lQR\operatorname{lQR} is 2 . For Camden, the mean and median are 65, the range is 4 , and the IQR is 2 . Use the measures of center and variation of these samples to select the person(s) to which each statement applies.
Heart Rate (bpm) \begin{tabular}{|l|l|l|} \cline { 2 - 3 } \multicolumn{1}{l|}{\begin{tabular}{l} This person is likely to have a lower heart \\ rate on a randomly selected day. \end{tabular}} & & Camden \\ \hline The line plot is symmetric. & & \\ \hline \begin{tabular}{l} This person is likely to have a higher heart \\ rate on a randomly selected day. \end{tabular} & & \\ \hline \begin{tabular}{l} The distribution of the data set is more \\ spread out. \end{tabular} & & \\ \hline \begin{tabular}{l} This person is more likely to have a heart \\ rate of 65 bpm on a randomly selected day. \end{tabular} & & \\ \hline \end{tabular}

Studdy Solution

STEP 1

What is this asking? We need to compare Camden's and Logan's heart rates using mean, median, range, and IQR to figure out who has a higher or lower heart rate on a random day, whose data is more spread out, and who is more likely to have a heart rate of 6565 bpm. Watch out! Don't mix up mean, median, range, and IQR!
Each tells us something different about the data.

STEP 2

1. Lower Heart Rate
2. Symmetry
3. Higher Heart Rate
4. Spread of Data
5. Heart Rate of 65 bpm

STEP 3

The **mean** heart rate for Camden is 6565 bpm, while Logan's is 7171 bpm.
Since 6565 is less than 7171, Camden is likely to have a lower heart rate on a randomly selected day.

STEP 4

Since the **mean** and **median** are the same for both Camden and Logan, both line plots are symmetric.

STEP 5

Logan's **mean** heart rate is 7171 bpm, while Camden's is 6565 bpm.
Since 7171 is greater than 6565, Logan is likely to have a higher heart rate on a randomly selected day.

STEP 6

The **range** of Logan's heart rates is 88 bpm, while Camden's is 44 bpm.
A larger range means the data is more spread out.
So, Logan's heart rate data is more spread out.

STEP 7

Camden's **mean** and **median** heart rate is 6565 bpm.
Since the data is symmetric, and centered around 6565, Camden is more likely to have a heart rate of 6565 bpm on a randomly selected day.

STEP 8

This person is likely to have a lower heart rate on a randomly selected day: **Camden** The line plot is symmetric: **Camden and Logan** This person is likely to have a higher heart rate on a randomly selected day: **Logan** The distribution of the data set is more spread out: **Logan** This person is more likely to have a heart rate of 65 bpm on a randomly selected day: **Camden**

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