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SHAPES OF DISTRIBUTIONS
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Name TWO variables that would likely form a normal distribution and ONE variable that would likely form a skewed distribution Note: do not use examples given in class, in the text, on the videos or in the examples below!! — think of something different for full credit.
(1) Normal distribution: Scores on the Scholastic Aptitude Test (scores are roughly symmetric around the mean) OR The number of raisins in Raisin Brand cereal boxes; OR the weight of Granny Smith applies. (You need only give two responses for the actual assignment.) Note that many variables in nature are approximately normally distributed — in the example of Granny Smith apples (green apples) there is no reason to assume there would be outliers on the high or low end.
(2) Skewed distributions: Distance traveled to school – positive skew (most people live fairly close — within a few miles, but occasionally a student is found who lives in Palmdale (as an example) – the student works near the college so he/she attends this school in the evening before driving home). The relatively few students who live very far away “skew” the distribution.
Another example could be “yards per carry” in football. Players may make a small amount of yardage “on the average” but occasionally make a long run that has a similar effect on the distribution as the student who lives far away.
Both examples above would form skewed distributions (positive skews in this case). You need only give TWO examples of a normal distribution and ONE example of a skewed distribution. Please keep your response to one sentence for each example.
Find a small set of REAL data (small sample size is preferred!). Tell me what the variable name is, show me the data, and report the mean, median & mode. This simple assignment is to be done with raw data (not grouped data). See chapter 4 in the text – it’s very simple. The variable can be something at home or data gathered elsewhere (e.g., the mean amount of time you spent on the internet last week; the mean number of points scored by professional sports teams in last Sunday’s games). See the hint below.
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