Question

1. the box plot displays the resting heart rate, in beats per minute (bpm), of 50 athletes taken five minutes after a workout. what percent of athletes have a resting heart rate above the median? what percent of athletes have a resting heart rate below the median? what percent of athletes have a resting heart rate below q1? what percent of athletes have a resting heart rate above q3? 7. find the mean of the data set. 2, 3, 3, 6, 7, 4, 1, 2 9. find the median for this data set. 8, 9, 6, 7, 8, 6, 4, 10

Explanation:

Step1: Recall box - plot properties

In a box - plot, the median divides the data into two equal parts. So, 50% of the data is above the median and 50% is below the median.

Step2: Recall quartile properties

Q1 is the first quartile, which means 25% of the data is below Q1. Q3 is the third quartile, which means 25% of the data is above Q3.

Step3: Calculate the mean of [2, 3, 3, 6, 7, 4, 1, 2]

The mean formula is $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}$. Here, $n = 8$, and $\sum_{i=1}^{8}x_{i}=2 + 3+3 + 6+7 + 4+1+2=28$. So, $\bar{x}=\frac{28}{8}=3.5$.

Step4: Calculate the median of [8, 9, 6, 7, 8, 6, 4, 10]

First, order the data set: [4, 6, 6, 7, 8, 8, 9, 10]. Since $n = 8$ (an even - numbered data set), the median is the average of the $\frac{n}{2}$th and $(\frac{n}{2}+1)$th ordered values. The $\frac{n}{2}=4$th value is 7 and the $(\frac{n}{2}+1)=5$th value is 8. So, the median is $\frac{7 + 8}{2}=7.5$.

Answer:

• What percent of athletes have a resting heart rate above the median? 50%
• What percent of athletes have a resting heart rate below the median? 50%
• What percent of athletes have a resting heart rate below Q1? 25%
• What percent of athletes have a resting heart rate above Q3? 25%
• Mean of [2, 3, 3, 6, 7, 4, 1, 2]: 3.5
• Median of [8, 9, 6, 7, 8, 6, 4, 10]: 7.5