MNITAB 2
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School
University Of Connecticut *
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Course
1000Q
Subject
Mathematics
Date
Apr 3, 2024
Type
Pages
3
Uploaded by PresidentHedgehog1140
Assignment 2 Please answer all ques2ons using the appropriate version of the dataset as assigned by your TA. Each graph must be labeled with a 2tle, axis labels, and a footnote with your name and sec2on number. 1. For this example, you will use a version of the datafile BASEBALL. This file contains the 2011 salaries for two major league baseball teams. C1 contains the salaries for one randomly selected MLB team, and C2 contains the salaries for a second randomly selected team. a. Use MINITAB to calculate the mean, median and standard devia2on for the salaries for each team. TEAM1 TEAM2 Team: Red Sox Team: Rangers Mean: 5093724 Mean: 4635037 Median: 1556250 Median: 3437500 Standard Devia2on: = 6311422 Standard Devia2on: 4728331 b. Which measure of central tendency, the mean or the median, do you think would give a more realis2c picture of the salaries? Write an explana2on jus2fying your choice. I think the median would give a more realis2c picture for both teams as there are a lot of outlying salaries given to superstars of the sport that would unachievable for almost all of the others. c. Use the means, medians and standard devia2ons of the two data sets to compare the two teams. Include comments on similari2es and differences in salaries. The mean of Red Sox is higher than the Rangers, however the median of the Rangers is higher than the Red Sox. This indicates that the Red Sox have many outliers outside of the upper fence and they are paying one or few of their players very big money, whereas the Rangers seem to be paying all of their players in closer range. This is further proven by the standard devia2on as the Red Sox have a standard devia2on much higher than the Rangers.
2. For this example, you will use a version of the datafile COLLEGE file. This file contains Math, Verbal and Wri2ng SAT scores. a. Construct a histogram for the Math SAT scores. Be sure to include a 2tle, X and Y axis labels, your name and your sec2on. b. Describe the shape of the distribu2on. This is a very symmetrical distribu2on. Probably as close as it can get to being symmetrical in a real world observa2on. c. Calculate the mean and standard devia2on of the Math scores. Mean = 589.31 Standard Devia2on: 52.7025 d. Calculate the intervals [
±
1s
]
, [
±
2s
]
, [
±
3s
]
. What percentage of the data would you expect to fall within each of these intervals? (You can use MINITAB or a hand calculator to calculate the intervals.) [
±
1s
] = 536.6075, 642.0125. 68% of
the
data
would
fall
within
these
intervals
[
±
2s
] = 483.905, 694.715. 95% of
the
data
would
fall
within
these
intervals
[
±
3s
] = 431.2025, 747.4175. 99.7% of
the
data
would
fall
within
these
intervals
x
x
x
x
x
x
e. Organize the data set into numerical order. What percentage of the data set actually did fall within the interval [
±
2s
]
? List the data points that did not lie in the interval. Values that did not make it: 434, 483, 721, 744. This means that 96% of the values were within the interval [
±
2s
].
f. Compare the means and standard devia2ons of the Math, Verbal and Wri2ng SAT scores. On average, on which of the two parts of the SAT test do students do befer? Students do befer usually on math and wri2ng Which set of scores has more variability? Verbal Which set had the lowest score? Verbal has the lowest average in terms of mean of 561.82. Verbal also has the lowest individual score of 407. Which set had the highest score? Math has the highest average in terms of mean of 589.31. Math also has the highest individual score of 744. x
x
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