Question

During the early part of the 1994 baseball season, many sports fans and baseball players noticed that the number of home runs being hit seemed to be unusually large. Below are separate stemplots for the number of home runs by American League and National League teams based on the team-by-team statistics on home runs hit through Friday, June 3, 1994 (from the Columbus Dispatch, Sunday, June 5, 1994). They are given as separate stemplots for the number of home runs by American and National League teams.
American League

2
3 5
4 0 3 9
5 1 4 7 8 8
6 4 8 8
7 5 7

National League

2 9
3 1
4 2 6 7 8 8
5 3 5 5 5
6 3 3 7
7

Required:
a. Find the median for the number of home runs hit through Friday, June 3, 1994 for the American League teams. Explain.
b. Find the mean of the number of home runs hit through Friday, June 3, 1994 by National League teams. Explain.

Answer 1

Answer:a

 a

    $m = 57.5$

b

   $\= x = 50.14$

Step-by-step explanation:

From the question we told that

  The stem plots for American League is

                  $2\\3\ \ \ \ \ 5\\4 \ \ \ \ \ 0\ 3 \ 9\\5 \ \ \ \ \ 1\ 4\ 7\ 8\ 8\\6 \ \ \ \ \ 4\ 8\ 8\\7 \ \ \ \ \ 5\ 7$

Here the first column  is the tens while each digit in the in the second column is the unit of the first column

  For example row 3 means

      40 , 43, 49

The  sample  size is  n = 14  

Generally the median is mathematically represented as

         $m = \frac{ K + Z}{2}$

Here  K is the $(\frac{n}{2}) th \ term \ in \ the \ data \ given$ i.e  $\frac{14}{2} = 7th \ term$

 From the stem plot the 7th term is  57

And

       K is the $(\frac{n}{2} + 1) th \ term \ in \ the \ data \ given$ i.e  $\frac{14}{2} + 1 = 8th \ term$

 From the stem plot the 8th term is  58

Thus the median is  

          $m = \frac{ 57 + 58}{2}$

=>       $m = 57.5$

The stem plots for National League is

            $2\ \ \ 9\\3\ \ \ \ 1\\4 \ \ \ \ 2\ 6\ 7\ 8\ 8\\5 \ \ \ \ 3\ 5\ 5\ 5\\6 \ \ \ \ 3\ 3\ 7\\7$

Generally the mean is mathematically evaluated as

           $\= x = \frac{\sum x_i}{n}$

           $\= x = \frac{29 + 31 + 42 + 46 + 47 + 48 + 48 + 53 + 55+ 55+ 55+ 63+ 63+ 67}{14}$

         $\= x = 50.14$