Question

3. Use "MLB_Salaries" data in Chapter3.xlsx to answer the following questions. For questions that require Excel, include the appropriate output (copy + paste) along with an explanation. Data description: An article in The Wall Street Journal (July 11, 2008) outlined a number of reasons as to why the 16 teams in Major League Baseball’s National League (NL) are inferior to the 14 teams in the American League (AL). One reason for the imbalance pointed to the disparity in opening-day payrolls: the average AL payroll is greater than the NL average. A portion of the data showing opening-day payroll (in $) for each team is shown in the accompanying table. Questions: a. Discuss the mean and the median of AL and NL opening-day salaries and comment on skewness. b. Compare the range and the standard deviation of AL and NL opening-day salaries. c. Use these summary measures to comment on the findings in The Wall Street Journal.

American League	Payroll	National League	Payroll
New York Yankees	206333389	Chicago Cubs	146609000
Boston Red Sox	162447333	Philadelphia Phillies	141928379
Detroit Tigers	122864928	New York Mets	134422942
Chicago White Sox	105530000	San Francisco Giants	98641333
Los Angeles Angels	104963866	Los Angeles Dodgers	95358016
Minnesota Twins	97559166	St. Louis Cardinals	93540751
Seattle Mariners	86510000	Houston Astros	92355500
Baltimore Orioles	81612500	Atlanta Braves	84423666
Tampa Bay Rays	71923471	Colorado Rockies	84227000
Kansas City Royals	71405210	Milwaukee Brewers	81108278
Toronto Blue Jays	62234000	Cincinnati Reds	71761542
Cleveland Indians	61203966	Washington Nationals	61400000
Texas Rangers	55250544	Arizona Diamondbacks	60718166
Oakland Athletics	51654900	Florida Marlins	57034719
		San Diego Padres	37799300
		Pittsburgh Pirates	34943000

Answer 1

a) Mean = Sum of all the data / Total no. of observations

Median = The median of a set of data is the middlemost number in the set. The median is also the number that is halfway into the set. To find the median, the data should first be arranged in order from least to greatest.

Standard deviation = σ= ( ∑(X−μ)2/N )0.5 μ - mean, n - total no. of observation , x - each data

Range = Maximum value - Minimum Value

Now from these formulas, I have found everything

American League	Payroll	National League	Payroll
New York Yankees	206333389	Chicago Cubs	146609000
Boston Red Sox	162447333	Philadelphia Phillies	141928379
Detroit Tigers	122864928	New York Mets	134422942
Chicago White Sox	105530000	San Francisco Giants	98641333
Los Angeles Angels	104963866	Los Angeles Dodgers	95358016
Minnesota Twins	97559166	St. Louis Cardinals	93540751
Seattle Mariners	86510000	Houston Astros	92355500
Baltimore Orioles	81612500	Atlanta Braves	84423666
Tampa Bay Rays	71923471	Colorado Rockies	84227000
Kansas City Royals	71405210	Milwaukee Brewers	81108278
Toronto Blue Jays	62234000	Cincinnati Reds	71761542
Cleveland Indians	61203966	Washington Nationals	61400000
Texas Rangers	55250544	Arizona Diamondbacks	60718166
Oakland Athletics	51654900	Florida Marlins	57034719
		San Diego Padres	37799300
		Pittsburgh Pirates	34943000
Mean	95820948.07	Mean	86016974.5
Median	84061250	Median	84325333
Range	154678489	Range	111666000
Standard deviation	43803002.27	Standard deviation	33403170.09

a) AL mean is greater than NL, but the median is greater of NL. Also in both the cases mean is greater than median so both are positively skewed.

Pearson’s Coefficient of Skewness. The formula is: if the median is given

Where = the mean, Md = the median and s = the standard deviation for the sample.

So skewness for AL = 0.81

skewness for NL = 0.15

Skewness is way higher for AL. These means that only few teams are earning most of the total income for AL. And NL has more symmetrical earning.

B) Range and Standard Deviation both are higher for AL. These also tell about more asymmetry in AL.

C) The wall street general is right the mean is high of AL. The mean (or average) is the most popular and well-known measure of central tendency. But the mean has one main disadvantage: it is particularly susceptible to the influence of outliers. These are values that are unusual compared to the rest of the data set by being especially small or large in numerical value. As we can see top teams of AL have way higher earnings than the rest of the team. As already discussed earning of AL is highly skewed. The other measure of central tendency, the median is almost the same for both the leagues because the median is less affected by outliers and skewed data. We can not argue only on the basis of mean that there is a disparity in opening day payrolls.