6-33. The United States Golf Association tests golf balls to ensure that they co

Question

6-33. The United States Golf Association tests golf balls to ensure that they conform to the rules of golf. Balls are tested for weight, diameter, roundness, and overall distance. The overall distance test is conducted by hitting balls with a driver swung by a mechanical device nicknamed "Iron Byron" after the leg- endary great Byron Nelson, whose swing the machine is said to emulate. Following are 100 distances (in meters) achieved by a particular brand of golf ball in the overall distance test. Construct a stem-and-leaf diagram for these data and comment on any important features that you notice. Compute the sam- ple mean, sample standard deviation, and the sample mediarn. What is the 90th percentile of distances? 235.2 233.4 239.1 243.5 246.7 235.2 229.1 255.3 232.2 243.4 229.5 242.0 240.6 228.2 210.8 2368

Explanation / Answer

number of observations =100

mean= sum of observations/number of observations

median = as the total number of observationsos even i.e. 100 median = 50th observation+51th observation/2

standard deviation = square root of variance , variance = [(observation1-mean)2    +(observation2-mean)2 ...........upto observation N]/N

90 percile - 90th percentile is the value of the 90th data value when data is set in acending order of their increasing value. in other 90% of the total observations will have less than or equal to 90th percentile value.

(only question 1, and data set is visible ,other images are not visible)

235.2 233.4 239.1 243.5 246.7 235.2 229.1 255.3 232.2 243.4 229.5 242 240.6 228.2 210.8 236.8 228.7 243.6 210.3 237.1 220.1 226.6 233.5 231.7 231.9 245.6 228.3 235.9 226.8 252.2 247.4 210.3 214.1 246.6 238.1 220.3 237.6 241.4 244.8 234.1 230.2 234.6 220.9 251.6 214 250.6 245.9 237.3 217.2 234.5 252.2 245.4 234.9 234 251.3 226.8 219.8 244.9 223.4 250.8 212.4 244.1 251.8 221 217.1 225.9 240.3 246.1 222.9 229.3 245.5 243.4 228.9 208.8 244.3 218.6 246.2 230.4 226.4 231.1 245.7 216.7 248.9 238.1 238.1 204.1 229.7 239.9 225.1 230.2 256.7 229.8 216.4 229.5 245.8 226.2 248.5 250 240.1 241.6 N = 100 sum of all the observations = 23423.9 mean= 234.239 standard deviation 11.75 median 239.5 90 percentile 250.28

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