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# Question: 1 in preparation for the australian open roger federer tested...

###### Question details

1. In preparation for the Australian Open, Roger Federer tested two different types of racquets from his major sponsor. Samples of 20 first serve times were recorded below using the two different types of racquets: Federer Control and Federer Prestige:

 Federer Control-FirstServeSpeeds (km/h) 206.80 205.40 200.70 208.57 198.96 203.18 200.90 209.09 199.95 203.18 201.01 212.35 200.03 203.76 202.70 213.21 200.54 208.10 221.76 218.34

 FedererPrestige -First Serve Speeds (km/h) 197.19 201.89 202.90 211.64 197.27 199.44 203.37 212.77 198.92 199.71 204.44 212.71 199.16 201.21 205.15 205.65 199.24 202.70 209.87 226.60

(a) Use EXCEL to obtain a histogram for each racquet. Use bin steps of size 5 starting from 195 through to 230 inclusive. (6 Marks)

(b) Use EXCEL to obtain Descriptive Statistics, Quartile 1 (Q1) and Quartile 3 (Q3) for each racquet. (6 Marks) EXCEL Instructions: Refer to Topic 7 in the Excel Booklet for instructions on how to obtain Descriptive Statistics and the two quartiles.

(c) Based on the histograms in (a), briefly describe the shape (symmetry, modality and outliers) of the data for each racquet. (8 Marks) Instructions for identifying outliers: Whether an observation is an outlier is a matter of judgement. One rule commonly used for identifying outliers is the so-called 1.5 × IQR rule. An observation is suspected to be an outlier if it lies more than 1.5 × IQR below the first quartile Q1 or above the third quartile Q3. Apply this rule to the data from each racquet. Identify suspected outliers (if any) by their exact value(s).

(d) Nominate appropriate measures of centrality and dispersion for the distribution of serving speeds for each racquet. Give reason(s) for your choice. For each distribution, give and interpret the values of the summary measures you have chosen. (8 Marks)

(e) On the basis of your results of (a)-(d), are there any differences between the two racquets? Write a paragraph based on your findings to Roger Federer in preparation for his upcoming Australian Open. (Use EXCEL Text Box) (6 Marks)