Question

One statistic calculated for pitchers in baseball is called the earned run average, or . The following boxplots summarize the for pitchers in two leagues, A and B.

Answer 1

Answer:

Step-by-step explanation:

One important statistic in baseball is a pitcher’s earned run average, or ERA. This number represents the average number of earned runs given up by the pitcher per nine innings. The following table lists the portion of the ERAs for pitchers playing for the New York Yankees and the Baltimore Orioles as of July 22, 2010; the complete data, labeled ERA , are available on the text website.

 New York

 Yankees ERA          Baltimore  Orioles ERA

 Sabathia 3.13        Guthrie                     4.58      

 Pettitte 2.88              Millwood                     5.77      

 Burnett 4.99              Matusz                      5.21      

 Hughes 3.99              Bergeson              6.51      

 Vazquez 4.68       Hernandez              4.29      

 Chamberlain 5.80        Berken 2.50      

 Gaudin 6.81             Hendrickson 5.23      

 Rivera 0.98           Albers 4.31      

 Robertson 4.86     Arrieta 4.87      

 Park 5.93        Simon 3.14      

 Mitre 2.88        Ohman 2.57      

 Logan 3.92        Tillman 7.92      

 Marte 4.08        Mata 7.79      

 Aceves 3.00        Meredith 5.40      

 Moseley 7.50        Uehara 2.92      

 Melancon 9.00        Castillo 10.13      

 Albaladejo 5.40        Johnson 6.52      

 Mickolio 7.36      

 Gonzalez 18.00      

a) Calculate the mean and the median ERAs for the New York Yankees. (Round your answers to 2 decimal places.)

Mean is the average sum of the numbers. It is expressed as;

$\overline x = \frac{\sum Xi}{N}$

Xi are the individual data

N is the sample size

From the data, the sample size for New York Yankees is 19

$\sum Xi = 3.13+2.88+4.99+3.99+4.68+5.8+6.81+0.98+4.86+5.93+2.88+3.92+4.08+3.00+7.50+9.00+5.40+7.36+18.00\\\\\sum Xi = 105.19\\\\\overline x = \frac{105.19}{19} \\\\\overline x = 5.54 (to \ 2dp)$

Median value is the value at the middle after re-arranging.. On rearranging in ascending order;

0.98, 2.88, 2.88, 3.00, 3.13, 3.92, 3.99, 4.08, 4.68)4.86(4.99, 5.40, 5.8, 5.93, 6.81, 7.36, 7.5, 9.00 18.00

Hence the median value is 4.86

   

b) Calculate the mean and the median ERAs for the Baltimore Orioles. (Round your answers to 2 decimal places.)

$\sum Xi =4.58+5.77+5.21+6.51+4.29+2.50+5.23+4.31+4.87+3.14+2.57+7.92+7.79+5.40+2.92+10.13+6.52\\\\\sum Xi = 89.66\\\\N = 17\\\\\overline x = \frac{89.66}{17} \\\overline x = 5.27 (to\ 2dp)$

For the median value:

Re-arrange the value in ascending order

2.50, 2.57, 2.92, 3.14, 4.29, 4.31, 4.58, 4.87)5.21(5.23, 5.40, 5.77, 6.51, 6.52, 7.79, 7.92, 10.13

Hence the median value is 5.21

     

c.) Based solely on your calculations above, which team is likely to have the better winning record?

The team that is likely to have the better winning record is the team with the highest mean value.

Since New York Yankees has the highest mean value of 5.54, hence the are likely to have the better winning record.