Question

1. In 1961, New York Yankee outfielder Roger Maris held the Major League record for home runs in a single season, with 61 home runs. That record held for 37 years. Here are Maris' home run totals for his 10 years in the American League.

    13 23 26    16    33    61    28    39    14    8

1. Find the mean number of home runs that Maris hit in a year.

2. Remove the record year. How does that affect his mean number of runs?

3. Find the median number of home runs that Maris hit in a year, both with and without his record 61. How does removing the record number of home runs affect his median number of runs?

4. If you had to choose between the mean and median to describe Maris' home run hitting pattern, which would you use?

Answer 1

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Ans: a). The mean is the average of values in the given data set Mean a year) Zixi 26/ = 26.1 10 Sum of all the observations/Ascember of obsevdios The mean number of home runs that manis hit in with his record GL is the mean number of home runs that moris hit in a year his record 61 is (13 +23+26+16+33+28+39 +14+)/10 without 200 200 9 .22 the number Removing El makes the mean number of his runs lower because at es an outlier that “s higher than all Other yuns. record 61 b) Median as the middle number in a sorted data set: The sorted daia set with record Glas as follows: 8, 13, 14, 16, 23, 26, 28, 38, 39, G] Median (n+1)/2 = (10+1)/2=1/2 = 5.5") valere in the above data set So, we take mean of 5" and om value le. (33+26))2 +24.5 is the median with record 61. The sorted data set without s as follows 8, 13, 14, 16,23,26,28133, 39 16 Median - (n+1)/2 = (9+1)/2 = 5 value in the above data Set 515) So, the above data set is 23 value in the Therefore, the median is 23 without the record 61 Removing the number 61 makes the median number of his runs lower because it is an outlier that Is higher than other runs C). If you had to choose between the mean and median to describe mari's home run hitting pattern II would choose the mean because the mean is us! usually better at showing distribution pattern than the median. all the