3) 3) As a professional golfer, you decide to experiment with two different golf
ID: 3321421 • Letter: 3
Question
3) 3) As a professional golfer, you decide to experiment with two different golf balls, Nike and Callaway. After the experiment, you will make a contract with one of the manufacturers and use their golf ball for the next year. The experiment consists of using the driver and hitting 200 golf balls of each type and measuring the distance traveled in yards. Your decision of which golf ball to use will be based upon consistency and maximal distance, both of which is valued in the game of golf The box and whisker plot for each manufacturer is shown below. Nike 245 250 255.5 266 280 Callaway 225 268.5 287 305 252 280 290 300 310 220 230 240 250 260 270 Yards a. How many Nike golf balls traveled less than 266 yards? b. How many Callaway golf balls traveled less than 252? c. Find the interquartile range for the Callaway data use it to find out if 225 yards is an outlier. d. Which golf ball would you choose to use and why?Explanation / Answer
(a)
266 yards is the third quartile (Q3) for the distance travelled by Nike golf balls.
Hence, 75% of the Nike golf balls have travelled less than 266 yards.
There were a total of 200 Nike golf balls.
So, 150 Nike golf balls have travelled less than 266 yards.
(b)
252 yards is the first quartile (Q1) for the distance travelled by Callaway golf balls.
Hence, 25% of the Callaway golf balls have travelled less than 266 yards.
There were a total of 200 Callaway golf balls.
So, 50 Callaway golf balls have travelled less than 252 yards.
(c)
For the Callaway data,
First quartile (Q1) = 252
Third quartile (Q3) = 287
Inter quartile range (IQR)
= Q3 - Q1
= 287 - 252
= 33
The lower non-oultier bound
= Q1 - 1.5 * IQR
= 252 - 1.5 * 33
= 202.5
Hence,
225 yards is not an outlier for the Callaway data.
(d)
The average distance traveeled by the Callaway golf ball is more than the Nike golf ball.
So, we would choose Callaway golf ball.
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