5. the box plot displays the resting heart rate, in beats per minute (bpm), of 50 athletes taken five…

5. 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

5. 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

Answer

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