Final answer:
The median for the given data is 43. The first quartile (Q1) is 41 and the third quartile (Q3) is 44. The interquartile range (IQR) is 3 and the range is 22. Your time of 3:34:10 in the marathon is faster than the median time.
Step-by-step explanation:
41. What is the median for this data, and how do you know?
The median for the given data is 43. To find the median, arrange the data in ascending order and then find the middle value. Since there are 10 contestants, the middle value will be the 5th value, which is 43.
42. What are the first and third quartiles for this data, and how do you know?
The first quartile (Q1) is the median of the lower half of the data, and the third quartile (Q3) is the median of the upper half of the data. To find Q1 and Q3, sort the data in ascending order and find the median(s) of the lower and upper halves. For this data, Q1 is 41 and Q3 is 44.
43. What is the interquartile range for this data?
The interquartile range (IQR) is the difference between the third quartile (Q3) and the first quartile (Q1). For this data, IQR = Q3 - Q1 = 44 - 41 = 3.
44. What is the range for this data?
The range is the difference between the largest and smallest values in the data. For this data, the range is 62 - 40 = 22.
45. In a marathon, the median finishing time was 3:35:04 (three hours, 35 minutes, and four seconds). You finished in 3:34:10. Interpret the meaning of the median time, and discuss your time in relation to it.
The median time represents the time at which half of the runners finished the marathon faster and half finished slower. Since your time of 3:34:10 is faster than the median time, it means that you did better than more than half of the runners in the race.