Describe the spread in running times based on quartiles. The data represents the average drive (in yards) for 186 professional golfers on the men’s PGA tour in 2011. The first quartile is 285.2 yards and third quartile is 297.5 yards.

Question
Describe the spread in running times based on quartiles.
The data represents the average drive (in yards) for 186 professional golfers on the men’s PGA tour in 2011. The first quartile is 285.2 yards and third quartile is 297.5 yards.

Answers (1)

2021-02-01
Calculation:
The first quartile \(Q_{1}\), is the value such that 25% of the observations are smaller and 75% are larger.
The second quartile \(Q_{2}\) is the value such that 50% of the observations are smaller and 50% are larger which is also called as the median.
The third quartile \(Q_{3}\), is the value such that 75% of the observations are smaller and 25% are larger.
The interquartile range is given below:
\(IQR=Q_{3}-Q_{1}\)
\(=297.5-285.2=12.3\)
Thus, middle 50% of the distribution with distance of the balls lies between the distance of 285.2 yards and 279.5 yards and that interquartile range as 12.3 yards.
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