Home Runs Essay

Submitted By 99Kassymarie
Words: 757
Pages: 4

1. Create a set of 5 positive numbers (repeats allowed) that has median 10 and mean 7.
What thought process did you use to create your numbers?
1, 2, 7, 10, 30
I picked 1, 2, and 7 as the first 3 numbers because they add up to 10, then 10 and 30 as 2 numbers bigger than 7 that add up to 40. That's a sum of 50 with no brain cells injured in the making. 2. Mary measures the weights of 5 newly hatched pythons in ounces. Here are Mary’s results: Python 12345
Mary 1.13oz1.02oz1.23oz1.06oz1.16oz
Calculate the mean and standard deviation of Mary’s measurements using the formula for each. 3. Use graphs and numerical summaries to describe how the following three datasets are similar, and how they are different.
a. 5, 7, 9, 11, 13, 15, 17
b. 5, 6, 7, 11, 15, 16, 17
c. 5, 5, 5, 11, 17, 17, 17

Each mean and median is 11. All 3 sets are symmetric. They all have the same min and max but different IQR’s and standard deviations.

4. I have a data set consisting of 33 whole number observations. Its five­number summary is (16, 20, 22, 30, 46).
a. What is the range of the data?
The range of the data is 30.
b. Tell what the five numbers in the five­number summary represent. Be specific.
Minimum= 16, Median= 22, Maximum= 46, Q1= 20 and Q3= 30
c. How many observations are strictly less than 22?
There are 16 observations that are strictly less than 20.
d. Is it possible that there is no observation equal to 22? Explain briefly.
No, it is possible not to get an observation of 22, because it is the median is the number in the middle. A data set containing 33 numbers only has one number in the middle.
e. How many observations are strictly less than 20?
There are 8 observations that are strictly less than 20.
f. Is it possible that there is no observation equal to 20? Explain briefly Yes, because 20 is Q1 which is the median of the first half half of the data. Since 16 numbers are in the first half of the data, the median will be the average of the 8th and 9th numbers.
g. Test for outliers. Are there any outliers Yes, their is an outlier. The outliner is 46 because it is greater than 45 which is the upper fence.
h. Approximately where is the mean? Briefly explain your reasoning.
The mean is greater than 22, which is the median, because the data is skewed right. 5. 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. Here are the data on the number of home runs hit by American and National League teams.
American League 35, 40, 43, 49, 51, 54, 57, 58, 58, 64, 68, 68, 75, 77
National League 29, 31, 42, 46, 47, 48, 48, 53, 55, 55, 55, 63, 63, 67
a. Construct box plots for comparing the number of home runs hit in the two leagues.

b. Calculate numerical summaries of the number of home runs hit in the two leagues.
Which of these numbers would be most appropriate for comparing the two leagues?
Explain.
The mean and standard deviation would be appropriate because the clump of high scores, the distribution is skewed to the left.
c. Are there any outliers in either of the…