Question

The following data represent weights (pounds) of a random sample of professional football players on the following teams.

X1 = weights of players for the Dallas Cowboys
X2 = weights of players for the Green Bay Packers
X3 = weights of players for the Denver Broncos
X4 = weights of players for the Miami Dolphins
X5 = weights of players for the San Francisco Forty Niners

You join a Fantasy Football league and you are wondering if weight is a factor in winning Football games.

Looking at the Summary output, which two teams have the biggest difference in weight?

See Attached Excel for Data.

Dallas Cowboys Wt.	Green Bay Packers Wt.	Denver Broncos Wt.	Miami Dolphins Wt.	San Fran. 49ers Wt.
250	260	270	260	247
255	271	250	255	249
255	258	281	265	255
264	263	273	257	247
250	267	257	268	244
265	254	264	263	245
245	255	233	247	249
252	250	254	253	260
266	248	268	251	217
246	240	252	252	208
251	254	256	266	228
263	275	265	264	253
248	270	252	210	249
228	225	256	236	223
221	222	235	225	221
223	230	216	230	228
220	225	241	232	271

Reference: The Sports Encyclopedia Pro Football

• A.Denver Broncos and San Francisco 49ers
• B. San Francisco 49ers and Miami Dolphins
• C. San Francisco 49ers and Green Bay Packers
• D. Denver Broncos and Miami Dolphins

Answer 1

The summary output can be obtained using the "Descriptive Statistic" function available in the data analysis package under the data tab of the MS-Excel and the results are :

Dallas Cowboys Wt.		Green Bay Packers Wt.		Denver Broncos Wt.		Miami Dolphins Wt.		San Fran. 49ers Wt.
Mean	247.1764706	Mean	251	Mean	254.2941176	Mean	249.0588235	Mean	240.8235
Standard Error	3.720210397	Standard Error	4.141788474	Standard Error	3.937717973	Standard Error	4.066063449	Standard Error	4.119747
Median	250	Median	254	Median	256	Median	253	Median	247
Mode	250	Mode	254	Mode	252	Mode	#N/A	Mode	249
Standard Deviation	15.33882042	Standard Deviation	17.07703136	Standard Deviation	16.23562713	Standard Deviation	16.76480908	Standard Deviation	16.98615
Sample Variance	235.2794118	Sample Variance	291.625	Sample Variance	263.5955882	Sample Variance	281.0588235	Sample Variance	288.5294
Kurtosis	-0.581442488	Kurtosis	-0.928392718	Kurtosis	0.636181835	Kurtosis	0.137422466	Kurtosis	-0.55481
Skewness	-0.725742052	Skewness	-0.490192016	Skewness	-0.682486675	Skewness	-0.958624665	Skewness	-0.36353
Range	46	Range	53	Range	65	Range	58	Range	63
Minimum	220	Minimum	222	Minimum	216	Minimum	210	Minimum	208
Maximum	266	Maximum	275	Maximum	281	Maximum	268	Maximum	271
Sum	4202	Sum	4267	Sum	4323	Sum	4234	Sum	4094
Count	17	Count	17	Count	17	Count	17	Count	17

The highest difference between two team averages are :

Denver Broncos Wt. - San Fran. 49ers Wt. = 254.2941176 - 240.8235 = 13.47062

Hope this answers your query!